Liu, Bocheng; Lu, Xuguang On the convergence to equilibrium for the spatially homogeneous Boltzmann equation for Fermi-Dirac particles. (English) Zbl 07745915 J. Stat. Phys. 190, No. 8, Paper No. 139, 36 p. (2023). MSC: 82Cxx 76Pxx 35Qxx PDFBibTeX XMLCite \textit{B. Liu} and \textit{X. Lu}, J. Stat. Phys. 190, No. 8, Paper No. 139, 36 p. (2023; Zbl 07745915) Full Text: DOI arXiv
Li, Yanchao; Zhong, Mingying Green’s function and pointwise behaviors of the one-dimensional modified Vlasov-Poisson-Boltzmann system. (English) Zbl 1517.76080 Kinet. Relat. Models 16, No. 5, 676-716 (2023). MSC: 76X05 76P05 35Q83 PDFBibTeX XMLCite \textit{Y. Li} and \textit{M. Zhong}, Kinet. Relat. Models 16, No. 5, 676--716 (2023; Zbl 1517.76080) Full Text: DOI arXiv
Briant, Marc Hypocoercivity for perturbation theory and perturbation of hypocoercivity for confined Boltzmann-type collisional equations. (English) Zbl 07699164 S\(\vec{\text{e}}\)MA J. 80, No. 1, 27-83 (2023). MSC: 35Q20 35Q35 35B20 35B65 82C40 76N15 80A19 PDFBibTeX XMLCite \textit{M. Briant}, S\(\vec{\text{e}}\)MA J. 80, No. 1, 27--83 (2023; Zbl 07699164) Full Text: DOI
Jiang, Ning; Luo, Yi-Long; Zhang, Teng-Fei Hydrodynamic limit of the incompressible Navier-Stokes-Fourier-Maxwell system with Ohm’s law from the Vlasov-Maxwell-Boltzmann system: Hilbert expansion approach. (English) Zbl 1516.35412 Arch. Ration. Mech. Anal. 247, No. 3, Paper No. 55, 85 p. (2023). MSC: 35Q83 35Q61 35Q20 35Q30 76D05 76W05 76P05 76X05 76T06 76N15 78A25 80A19 PDFBibTeX XMLCite \textit{N. Jiang} et al., Arch. Ration. Mech. Anal. 247, No. 3, Paper No. 55, 85 p. (2023; Zbl 1516.35412) Full Text: DOI arXiv
Fang, Zhendong; Jiang, Ning Convergence from the two-species Vlasov-Poisson-Boltzmann system to the two-fluid incompressible Navier-Stokes-Fourier-Poisson system with Ohm’s law. (English) Zbl 1524.76356 Acta Math. Sci., Ser. B, Engl. Ed. 43, No. 2, 777-820 (2023). MSC: 76P05 82C40 82D05 76T99 PDFBibTeX XMLCite \textit{Z. Fang} and \textit{N. Jiang}, Acta Math. Sci., Ser. B, Engl. Ed. 43, No. 2, 777--820 (2023; Zbl 1524.76356) Full Text: DOI
He, Ling-Bing; Jiang, Jin-Cheng On the Cauchy problem for the cutoff Boltzmann equation with small initial data. (English) Zbl 1506.35134 J. Stat. Phys. 190, No. 3, Paper No. 52, 25 p. (2023). MSC: 35Q20 82C40 35A01 35A02 35B65 PDFBibTeX XMLCite \textit{L.-B. He} and \textit{J.-C. Jiang}, J. Stat. Phys. 190, No. 3, Paper No. 52, 25 p. (2023; Zbl 1506.35134) Full Text: DOI arXiv
Fang, Zhendong; Wang, Hao Convergence from two-species Vlasov-Poisson-Boltzmann system to two-fluid incompressible Navier-Stokes-Fourier-Poisson system. (English) Zbl 1520.76106 Discrete Contin. Dyn. Syst., Ser. B 27, No. 8, 4347-4386 (2022). Reviewer: Stephen Wollman (New York) MSC: 76X05 76P05 76D03 35Q83 35Q20 35Q30 PDFBibTeX XMLCite \textit{Z. Fang} and \textit{H. Wang}, Discrete Contin. Dyn. Syst., Ser. B 27, No. 8, 4347--4386 (2022; Zbl 1520.76106) Full Text: DOI arXiv
Jang, Jin Woo; Strain, Robert M. Asymptotic stability of the relativistic Boltzmann equation without angular cut-off. (English) Zbl 1497.35333 Ann. PDE 8, No. 2, Paper No. 20, 167 p. (2022). MSC: 35Q20 35R11 76P05 83A05 82C40 35B65 26A33 PDFBibTeX XMLCite \textit{J. W. Jang} and \textit{R. M. Strain}, Ann. PDE 8, No. 2, Paper No. 20, 167 p. (2022; Zbl 1497.35333) Full Text: DOI arXiv
Jiang, Ning; Luo, Yi-Long From Vlasov-Maxwell-Boltzmann system to two-fluid incompressible Navier-Stokes-Fourier-Maxwell system with Ohm’s law: convergence for classical solutions. (English) Zbl 1507.35288 Ann. PDE 8, No. 1, Paper No. 4, 126 p. (2022). MSC: 35Q83 35Q61 35Q20 35Q30 76W05 80A19 35A01 35A09 PDFBibTeX XMLCite \textit{N. Jiang} and \textit{Y.-L. Luo}, Ann. PDE 8, No. 1, Paper No. 4, 126 p. (2022; Zbl 1507.35288) Full Text: DOI arXiv
Lasarzik, Robert Maximally dissipative solutions for incompressible fluid dynamics. (English) Zbl 1497.35345 Z. Angew. Math. Phys. 73, No. 1, Paper No. 1, 21 p. (2022). Reviewer: Gelu Paşa (Bucureşti) MSC: 35Q30 35Q31 76D05 35D30 35B65 35A01 35A02 49M41 PDFBibTeX XMLCite \textit{R. Lasarzik}, Z. Angew. Math. Phys. 73, No. 1, Paper No. 1, 21 p. (2022; Zbl 1497.35345) Full Text: DOI arXiv
Li, Hai-Liang; Yang, Tong; Zhong, Mingying Diffusion limit of the Vlasov-Poisson-Boltzmann system. (English) Zbl 1479.76121 Kinet. Relat. Models 14, No. 2, 211-255 (2021). MSC: 76X05 35Q83 35Q20 PDFBibTeX XMLCite \textit{H.-L. Li} et al., Kinet. Relat. Models 14, No. 2, 211--255 (2021; Zbl 1479.76121) Full Text: DOI arXiv
Lasarzik, Robert Analysis of a thermodynamically consistent Navier-Stokes-Cahn-Hilliard model. (English) Zbl 1479.35676 Nonlinear Anal., Theory Methods Appl., Ser. A, Theory Methods 213, Article ID 112526, 33 p. (2021). MSC: 35Q35 35D35 76D05 35A01 35B65 PDFBibTeX XMLCite \textit{R. Lasarzik}, Nonlinear Anal., Theory Methods Appl., Ser. A, Theory Methods 213, Article ID 112526, 33 p. (2021; Zbl 1479.35676) Full Text: DOI arXiv
Jang, Jin Woo; Strain, Robert M.; Yun, Seok-Bae Propagation of uniform upper bounds for the spatially homogeneous relativistic Boltzmann equation. (English) Zbl 1467.76049 Arch. Ration. Mech. Anal. 241, No. 1, 149-186 (2021). MSC: 76P05 76Y05 35Q20 83C55 PDFBibTeX XMLCite \textit{J. W. Jang} et al., Arch. Ration. Mech. Anal. 241, No. 1, 149--186 (2021; Zbl 1467.76049) Full Text: DOI arXiv
He, Ling-Bing; Jiang, Jin-Cheng; Zhou, Yu-Long On the cutoff approximation for the Boltzmann equation with long-range interaction. (English) Zbl 1460.35249 J. Stat. Phys. 181, No. 5, 1817-1905 (2020). MSC: 35Q20 35A01 35A02 35A09 PDFBibTeX XMLCite \textit{L.-B. He} et al., J. Stat. Phys. 181, No. 5, 1817--1905 (2020; Zbl 1460.35249) Full Text: DOI
Jiang, Jin-Cheng Sharp regularizing estimates for the gain term of the Boltzmann collision operator. (English) Zbl 1448.35354 SIAM J. Math. Anal. 52, No. 4, 4068-4100 (2020). MSC: 35Q20 35S30 35B65 PDFBibTeX XMLCite \textit{J.-C. Jiang}, SIAM J. Math. Anal. 52, No. 4, 4068--4100 (2020; Zbl 1448.35354) Full Text: DOI arXiv
Xiao, Tianbai; Liu, Chang; Xu, Kun; Cai, Qingdong A velocity-space adaptive unified gas kinetic scheme for continuum and rarefied flows. (English) Zbl 1440.76139 J. Comput. Phys. 415, Article ID 109535, 34 p. (2020). MSC: 76P05 76L05 65M70 PDFBibTeX XMLCite \textit{T. Xiao} et al., J. Comput. Phys. 415, Article ID 109535, 34 p. (2020; Zbl 1440.76139) Full Text: DOI arXiv
Hu, Jingwei; Ma, Zheng A fast spectral method for the inelastic Boltzmann collision operator and application to heated granular gases. (English) Zbl 1451.76140 J. Comput. Phys. 385, 119-134 (2019). MSC: 76T25 65M70 65T50 76P05 35Q20 35R09 PDFBibTeX XMLCite \textit{J. Hu} and \textit{Z. Ma}, J. Comput. Phys. 385, 119--134 (2019; Zbl 1451.76140) Full Text: DOI
Jiang, Jin-Cheng; Liu, Tai-Ping Boltzmann collision operator for the infinite range potential: a limit problem. (English) Zbl 1423.35292 Ann. Inst. Henri Poincaré, Anal. Non Linéaire 36, No. 6, 1639-1677 (2019). Reviewer: Eugene Postnikov (Kursk) MSC: 35Q20 76P05 PDFBibTeX XMLCite \textit{J.-C. Jiang} and \textit{T.-P. Liu}, Ann. Inst. Henri Poincaré, Anal. Non Linéaire 36, No. 6, 1639--1677 (2019; Zbl 1423.35292) Full Text: DOI
Jang, Jin Woo; Yun, Seok-Bae Gain of regularity for the relativistic collision operator. (English) Zbl 1408.81034 Appl. Math. Lett. 90, 162-169 (2019). MSC: 81V70 81U20 35Q20 70H40 47A50 PDFBibTeX XMLCite \textit{J. W. Jang} and \textit{S.-B. Yun}, Appl. Math. Lett. 90, 162--169 (2019; Zbl 1408.81034) Full Text: DOI arXiv
Lasarzik, Robert Dissipative solution to the Ericksen-Leslie system equipped with the Oseen-Frank energy. (English) Zbl 1406.35286 Z. Angew. Math. Phys. 70, No. 1, Paper No. 8, 39 p. (2019). MSC: 35Q35 35K55 35R06 35R45 76A15 35B40 76W05 PDFBibTeX XMLCite \textit{R. Lasarzik}, Z. Angew. Math. Phys. 70, No. 1, Paper No. 8, 39 p. (2019; Zbl 1406.35286) Full Text: DOI arXiv
Löbus, Jörg-Uwe Boundedness of the stationary solution to the Boltzmann equation with spatial smearing, diffusive boundary conditions, and Lions’ collision kernel. (English) Zbl 1408.35116 SIAM J. Math. Anal. 50, No. 6, 5761-5782 (2018). Reviewer: Alain Brillard (Riedisheim) MSC: 35Q20 76P05 PDFBibTeX XMLCite \textit{J.-U. Löbus}, SIAM J. Math. Anal. 50, No. 6, 5761--5782 (2018; Zbl 1408.35116) Full Text: DOI arXiv
Bennett, Jonathan; Bez, Neal; Flock, Taryn C.; Gutiérrez, Susana; Iliopoulou, Marina A sharp \(k\)-plane Strichartz inequality for the Schrödinger equation. (English) Zbl 1393.42026 Trans. Am. Math. Soc. 370, No. 8, 5617-5633 (2018). Reviewer: Michael Perelmuter (Kyïv) MSC: 42B37 35A23 PDFBibTeX XMLCite \textit{J. Bennett} et al., Trans. Am. Math. Soc. 370, No. 8, 5617--5633 (2018; Zbl 1393.42026) Full Text: DOI arXiv
Hundertmark, Dirk; Lee, Young-Ran Why do solutions of the Maxwell-Boltzmann equation tend to be Gaussians? A simple answer. (English) Zbl 1377.39035 Doc. Math. 22, 1267-1273 (2017). MSC: 39B32 82C40 PDFBibTeX XMLCite \textit{D. Hundertmark} and \textit{Y.-R. Lee}, Doc. Math. 22, 1267--1273 (2017; Zbl 1377.39035) Full Text: DOI
Gamba, Irene M.; Haack, Jeffrey R.; Hauck, Cory D.; Hu, Jingwei A fast spectral method for the Boltzmann collision operator with general collision kernels. (English) Zbl 1394.35310 SIAM J. Sci. Comput. 39, No. 4, B658-B674 (2017). Reviewer: Catalin Popa (Iaşi) MSC: 35Q20 65M70 65T50 PDFBibTeX XMLCite \textit{I. M. Gamba} et al., SIAM J. Sci. Comput. 39, No. 4, B658--B674 (2017; Zbl 1394.35310) Full Text: DOI arXiv
Barbaroux, Jean-Marie; Hundertmark, Dirk; Ried, Tobias; Vugalter, Semjon Gevrey smoothing for weak solutions of the fully nonlinear homogeneous Boltzmann and Kac equations without cutoff for Maxwellian molecules. (English) Zbl 1382.35177 Arch. Ration. Mech. Anal. 225, No. 2, 601-661 (2017). Reviewer: Dmitry Pelinovsky (Hamilton) MSC: 35Q20 35B65 35D30 35R11 PDFBibTeX XMLCite \textit{J.-M. Barbaroux} et al., Arch. Ration. Mech. Anal. 225, No. 2, 601--661 (2017; Zbl 1382.35177) Full Text: DOI arXiv HAL
Hu, Jingwei; Jin, Shi A stochastic Galerkin method for the Boltzmann equation with uncertainty. (English) Zbl 1349.82088 J. Comput. Phys. 315, 150-168 (2016). MSC: 82C80 65M75 45K05 82C40 PDFBibTeX XMLCite \textit{J. Hu} and \textit{S. Jin}, J. Comput. Phys. 315, 150--168 (2016; Zbl 1349.82088) Full Text: DOI
Liu, Chang; Xu, Kun; Sun, Quanhua; Cai, Qingdong A unified gas-kinetic scheme for continuum and rarefied flows. IV: Full Boltzmann and model equations. (English) Zbl 1349.82055 J. Comput. Phys. 314, 305-340 (2016). MSC: 82C40 76M28 76P05 PDFBibTeX XMLCite \textit{C. Liu} et al., J. Comput. Phys. 314, 305--340 (2016; Zbl 1349.82055) Full Text: DOI arXiv
Arkeryd, Leif; Nouri, Anne Well-posedness of the Cauchy problem for a space-dependent anyon Boltzmann equation. (English) Zbl 1341.82047 SIAM J. Math. Anal. 47, No. 6, 4720-4742 (2015). Reviewer: Bassano Vacchini (Milano) MSC: 82C05 82C40 82C22 35Q20 PDFBibTeX XMLCite \textit{L. Arkeryd} and \textit{A. Nouri}, SIAM J. Math. Anal. 47, No. 6, 4720--4742 (2015; Zbl 1341.82047) Full Text: DOI arXiv
Cho, Yong-Kum On the homogeneous Boltzmann equation with soft-potential collision kernels. (English) Zbl 1328.35142 Kinet. Relat. Models 8, No. 2, 309-333 (2015). MSC: 35Q20 35B65 35Q82 47G20 76P05 82B40 PDFBibTeX XMLCite \textit{Y.-K. Cho}, Kinet. Relat. Models 8, No. 2, 309--333 (2015; Zbl 1328.35142) Full Text: DOI
Lu, Xuguang; Mouhot, Clément On measure solutions of the Boltzmann equation. II: Rate of convergence to equilibrium. (English) Zbl 1311.35181 J. Differ. Equations 258, No. 11, 3742-3810 (2015). MSC: 35Q20 76P05 35J05 35J10 35K05 35L05 82B40 82C40 82D05 35B35 35B65 PDFBibTeX XMLCite \textit{X. Lu} and \textit{C. Mouhot}, J. Differ. Equations 258, No. 11, 3742--3810 (2015; Zbl 1311.35181) Full Text: DOI arXiv
Dimarco, G.; Pareschi, L. Numerical methods for kinetic equations. (English) Zbl 1398.65260 Acta Numerica 23, 369-520 (2014). MSC: 65M75 76P05 82D10 PDFBibTeX XMLCite \textit{G. Dimarco} and \textit{L. Pareschi}, Acta Numerica 23, 369--520 (2014; Zbl 1398.65260) Full Text: DOI
Prasath, V. B. Surya; Vorotnikov, D. On a system of adaptive coupled PDEs for image restoration. (English) Zbl 1295.35254 J. Math. Imaging Vis. 48, No. 1, 35-52 (2014). MSC: 35K51 94A08 35K59 PDFBibTeX XMLCite \textit{V. B. S. Prasath} and \textit{D. Vorotnikov}, J. Math. Imaging Vis. 48, No. 1, 35--52 (2014; Zbl 1295.35254) Full Text: DOI arXiv
Saint-Raymond, Laure A mathematical PDE perspective on the Chapman-Enskog expansion. (English) Zbl 1295.35353 Bull. Am. Math. Soc., New Ser. 51, No. 2, 247-275 (2014). Reviewer: Alexander Mikhajlovich Blokhin (Novosibirsk) MSC: 35Q20 35C20 76P05 82C40 PDFBibTeX XMLCite \textit{L. Saint-Raymond}, Bull. Am. Math. Soc., New Ser. 51, No. 2, 247--275 (2014; Zbl 1295.35353) Full Text: DOI
Arkeryd, Leif On low temperature kinetic theory; spin diffusion, Bose Einstein condensates, anyons. (English) Zbl 1276.82048 J. Stat. Phys. 150, No. 6, 1063-1079 (2013). Reviewer: Oleg A. Sinkevich (Moskva) MSC: 82C40 82D50 76Y05 82D30 35Q60 35Q55 PDFBibTeX XMLCite \textit{L. Arkeryd}, J. Stat. Phys. 150, No. 6, 1063--1079 (2013; Zbl 1276.82048) Full Text: DOI arXiv
Zheng, Min Ling; Yang, Xiao Ping Viscosity analysis on the Boltzmann equation. (English) Zbl 1253.35133 Acta Math. Sin., Engl. Ser. 28, No. 10, 2139-2152 (2012). MSC: 35Q35 35Q20 76P05 82C40 PDFBibTeX XMLCite \textit{M. L. Zheng} and \textit{X. P. Yang}, Acta Math. Sin., Engl. Ser. 28, No. 10, 2139--2152 (2012; Zbl 1253.35133) Full Text: DOI
Alexandre, R.; Morimoto, Y.; Ukai, S.; Xu, C.-J.; Yang, T. The Boltzmann equation without angular cutoff in the whole space. I: global existence for soft potential. (English) Zbl 1232.35110 J. Funct. Anal. 262, No. 3, 915-1010 (2012). MSC: 35Q20 82C40 35A01 PDFBibTeX XMLCite \textit{R. Alexandre} et al., J. Funct. Anal. 262, No. 3, 915--1010 (2012; Zbl 1232.35110) Full Text: DOI arXiv
Andréasson, Håkan The Einstein-Vlasov system/kinetic theory. (English) Zbl 1316.83021 Living Rev. Relativ. 14, Article No. 2011-4, 55 p. (2011). MSC: 83C05 83C55 83-02 PDFBibTeX XMLCite \textit{H. Andréasson}, Living Rev. Relativ. 14, Article No. 2011--4, 55 p. (2011; Zbl 1316.83021) Full Text: DOI arXiv
Kim, Chanwoo Formation and propagation of discontinuity for Boltzmann equation in non-convex domains. (English) Zbl 1237.35126 Commun. Math. Phys. 308, No. 3, 641-701 (2011). Reviewer: Giovanni Mascali (Arcavacata di Rende) MSC: 35Q20 76P05 35L67 35A21 PDFBibTeX XMLCite \textit{C. Kim}, Commun. Math. Phys. 308, No. 3, 641--701 (2011; Zbl 1237.35126) Full Text: DOI arXiv
Lu, Xuguang; Zhang, Xiangdong On the Boltzmann equation for 2D Bose-Einstein particles. (English) Zbl 1222.82068 J. Stat. Phys. 143, No. 5, 990-1019 (2011). Reviewer: Guy Jumarie (Montréal) MSC: 82C40 82B10 76P05 PDFBibTeX XMLCite \textit{X. Lu} and \textit{X. Zhang}, J. Stat. Phys. 143, No. 5, 990--1019 (2011; Zbl 1222.82068) Full Text: DOI
Gressman, Philip T.; Strain, Robert M. Global classical solutions of the Boltzmann equation without angular cut-off. (English) Zbl 1248.35140 J. Am. Math. Soc. 24, No. 3, 771-847 (2011). MSC: 35Q20 35R11 35Q82 76P05 82C40 35H20 35B65 26A33 PDFBibTeX XMLCite \textit{P. T. Gressman} and \textit{R. M. Strain}, J. Am. Math. Soc. 24, No. 3, 771--847 (2011; Zbl 1248.35140) Full Text: DOI arXiv
Alexandre, R.; Morimoto, Y.; Ukai, S.; Xu, C.-J.; Yang, T. Global existence and full regularity of the Boltzmann equation without angular cutoff. (English) Zbl 1230.35082 Commun. Math. Phys. 304, No. 2, 513-581 (2011). Reviewer: Argiris I. Delis (Chania) MSC: 35Q20 35A09 35B65 82C40 PDFBibTeX XMLCite \textit{R. Alexandre} et al., Commun. Math. Phys. 304, No. 2, 513--581 (2011; Zbl 1230.35082) Full Text: DOI arXiv
Filbet, Francis; Mouhot, Clément Analysis of spectral methods for the homogeneous Boltzmann equation. (English) Zbl 1213.82069 Trans. Am. Math. Soc. 363, No. 4, 1947-1980 (2011). MSC: 82C40 65M70 76P05 PDFBibTeX XMLCite \textit{F. Filbet} and \textit{C. Mouhot}, Trans. Am. Math. Soc. 363, No. 4, 1947--1980 (2011; Zbl 1213.82069) Full Text: DOI arXiv
Arsénio, Diogo On the global existence of mild solutions to the Boltzmann equation for small data in \(L^D\). (English) Zbl 1209.35094 Commun. Math. Phys. 302, No. 2, 453-476 (2011). MSC: 35Q20 76P05 35B45 35A01 PDFBibTeX XMLCite \textit{D. Arsénio}, Commun. Math. Phys. 302, No. 2, 453--476 (2011; Zbl 1209.35094) Full Text: DOI
Chen, Yemin Smoothing effects for weak solutions of the spatially homogeneous Landau-Fermi-Dirac equation for hard potentials. (English) Zbl 1205.35316 Acta Appl. Math. 113, No. 1, 101-116 (2011). MSC: 35Q82 35D30 35B65 82C31 PDFBibTeX XMLCite \textit{Y. Chen}, Acta Appl. Math. 113, No. 1, 101--116 (2011; Zbl 1205.35316) Full Text: DOI
Tadmon, Calvin Non-negativity of the solution of the Boltzmann equation in a curved space-time. (English) Zbl 1245.82025 Afr. Diaspora J. Math. 10, No. 1, 23-38 (2010). MSC: 82B40 82C40 83A05 PDFBibTeX XMLCite \textit{C. Tadmon}, Afr. Diaspora J. Math. 10, No. 1, 23--38 (2010; Zbl 1245.82025) Full Text: Euclid
Arkeryd, L. A quantum Boltzmann equation for Haldane statistics and hard forces; the space-homogeneous initial value problem. (English) Zbl 1203.82008 Commun. Math. Phys. 298, No. 2, 573-583 (2010). MSC: 82B10 76P05 82C22 35Q20 PDFBibTeX XMLCite \textit{L. Arkeryd}, Commun. Math. Phys. 298, No. 2, 573--583 (2010; Zbl 1203.82008) Full Text: DOI
Tsuji, Tetsuro; Aoki, Kazuo; Golse, François Relaxation of a free-molecular gas to equilibrium caused by interaction with Vessel wall. (English) Zbl 1203.76134 J. Stat. Phys. 140, No. 3, 518-543 (2010). Reviewer: Oleg A. Sinkevich (Moskva) MSC: 76P05 82C40 81V55 PDFBibTeX XMLCite \textit{T. Tsuji} et al., J. Stat. Phys. 140, No. 3, 518--543 (2010; Zbl 1203.76134) Full Text: DOI Link
Levermore, C. David; Masmoudi, Nader From the Boltzmann equation to an incompressible Navier-Stokes-Fourier system. (English) Zbl 1304.35476 Arch. Ration. Mech. Anal. 196, No. 3, 753-809 (2010). MSC: 35Q20 35Q35 76D05 76P05 82C40 PDFBibTeX XMLCite \textit{C. D. Levermore} and \textit{N. Masmoudi}, Arch. Ration. Mech. Anal. 196, No. 3, 753--809 (2010; Zbl 1304.35476) Full Text: DOI
Gamba, I. M.; Panferov, V.; Villani, C. Upper Maxwellian bounds for the spatially homogeneous Boltzmann equation. (English) Zbl 1273.76373 Arch. Ration. Mech. Anal. 194, No. 1, 253-282 (2009). MSC: 76P05 82B40 PDFBibTeX XMLCite \textit{I. M. Gamba} et al., Arch. Ration. Mech. Anal. 194, No. 1, 253--282 (2009; Zbl 1273.76373) Full Text: DOI arXiv
Bosi, Roberta; Cáceres, Maria J. The BGK model with external confining potential: existence, long-time behaviour and time-periodic Maxwellian equilibria. (English) Zbl 1188.82060 J. Stat. Phys. 136, No. 2, 297-330 (2009). Reviewer: Oleg A. Sinkevich (Moskva) MSC: 82C40 76P05 35Q20 35Q35 82B40 82D05 PDFBibTeX XMLCite \textit{R. Bosi} and \textit{M. J. Cáceres}, J. Stat. Phys. 136, No. 2, 297--330 (2009; Zbl 1188.82060) Full Text: DOI
Chen, Yemin; Desvillettes, Laurent; He, Lingbing Smoothing effects for classical solutions of the full Landau equation. (English) Zbl 1169.76064 Arch. Ration. Mech. Anal. 193, No. 1, 21-55 (2009). MSC: 76X05 35Q35 35Q60 PDFBibTeX XMLCite \textit{Y. Chen} et al., Arch. Ration. Mech. Anal. 193, No. 1, 21--55 (2009; Zbl 1169.76064) Full Text: DOI
Carlen, Eric A.; Carvalho, Maria C.; Lu, Xuguang On strong convergence to equilibrium for the Boltzmann equation with soft potentials. (English) Zbl 1191.76087 J. Stat. Phys. 135, No. 4, 681-736 (2009). Reviewer: Oleg A. Sinkevich (Moskva) MSC: 76P05 82C40 45K05 PDFBibTeX XMLCite \textit{E. A. Carlen} et al., J. Stat. Phys. 135, No. 4, 681--736 (2009; Zbl 1191.76087) Full Text: DOI arXiv
Bisi, Marzia; Carrillo, José A.; Lods, Bertrand Equilibrium solution to the inelastic Boltzmann equation driven by a particle bath. (English) Zbl 1161.82017 J. Stat. Phys. 133, No. 5, 841-870 (2008). MSC: 82C40 76P05 82C22 PDFBibTeX XMLCite \textit{M. Bisi} et al., J. Stat. Phys. 133, No. 5, 841--870 (2008; Zbl 1161.82017) Full Text: DOI arXiv
Lu, Xuguang On the Boltzmann equation for Fermi-Dirac particles with very soft potentials: global existence of weak solutions. (English) Zbl 1167.35007 J. Differ. Equations 245, No. 7, 1705-1761 (2008). MSC: 35F20 82C99 76P05 PDFBibTeX XMLCite \textit{X. Lu}, J. Differ. Equations 245, No. 7, 1705--1761 (2008; Zbl 1167.35007) Full Text: DOI
Heintz, Alexei; Kowalczyk, Piotr; Grzhibovskis, Richards Fast numerical method for the Boltzmann equation on non-uniform grids. (English) Zbl 1141.82328 J. Comput. Phys. 227, No. 13, 6681-6695 (2008). MSC: 82C40 76P05 65T50 65M50 PDFBibTeX XMLCite \textit{A. Heintz} et al., J. Comput. Phys. 227, No. 13, 6681--6695 (2008; Zbl 1141.82328) Full Text: DOI
Kirsch, R.; Rjasanow, S. A weak formulation of the Boltzmann equation based on the Fourier transform. (English) Zbl 1141.82014 J. Stat. Phys. 129, No. 3, 483-492 (2007). Reviewer: Oleg A. Sinkevich (Moskva) MSC: 82C40 76P05 82D05 PDFBibTeX XMLCite \textit{R. Kirsch} and \textit{S. Rjasanow}, J. Stat. Phys. 129, No. 3, 483--492 (2007; Zbl 1141.82014) Full Text: DOI
Glassey, Robert T. Global solutions to the Cauchy problem for the relativistic Boltzmann equation with near-vacuum data. (English) Zbl 1107.82047 Commun. Math. Phys. 264, No. 3, 705-724 (2006). MSC: 82C40 76P05 76Y05 35Q75 35F25 PDFBibTeX XMLCite \textit{R. T. Glassey}, Commun. Math. Phys. 264, No. 3, 705--724 (2006; Zbl 1107.82047) Full Text: DOI
Mischler, S.; Mouhot, C. Cooling process for inelastic Boltzmann equations for hard spheres. II: Self-similar solutions and tail behavior. (English) Zbl 1135.82030 J. Stat. Phys. 124, No. 2-4, 703-746 (2006). MSC: 82C40 82D05 82B40 76P05 PDFBibTeX XMLCite \textit{S. Mischler} and \textit{C. Mouhot}, J. Stat. Phys. 124, No. 2--4, 703--746 (2006; Zbl 1135.82030) Full Text: DOI arXiv
Mouhot, Clément Rate of convergence to equilibrium for the spatially homogeneous Boltzmann equation with hard potentials. (English) Zbl 1113.82062 Commun. Math. Phys. 261, No. 3, 629-672 (2006). MSC: 82C40 47N55 PDFBibTeX XMLCite \textit{C. Mouhot}, Commun. Math. Phys. 261, No. 3, 629--672 (2006; Zbl 1113.82062) Full Text: DOI arXiv
Biryuk, Andrei; Craig, Walter; Panferov, Vladislav Strong solutions of the Boltzmann equation in one spatial dimension. (English) Zbl 1096.35001 C. R., Math., Acad. Sci. Paris 342, No. 11, 843-848 (2006). MSC: 35A05 76P05 PDFBibTeX XMLCite \textit{A. Biryuk} et al., C. R., Math., Acad. Sci. Paris 342, No. 11, 843--848 (2006; Zbl 1096.35001) Full Text: DOI
Rendall, Alan D. Theorems on existence and global dynamics for the Einstein equations. (English) Zbl 1316.83008 Living Rev. Relativ. 8, Article No. 2005-6, 68 p. (2005). MSC: 83-02 83C15 83C05 83A05 83C75 PDFBibTeX XMLCite \textit{A. D. Rendall}, Living Rev. Relativ. 8, Article No. 2005--6, 68 p. (2005; Zbl 1316.83008) Full Text: DOI arXiv
Fournier, Nicolas; Mischler, Stéphane A spatially homogeneous Boltzmann equation for elastic, inelastic and coalescing collisions. (English) Zbl 1088.82021 J. Math. Pures Appl., IX. Sér. 84, No. 9, 1173-1234 (2005). Reviewer: Guy Jumarie (Montréal) MSC: 82C40 60J75 PDFBibTeX XMLCite \textit{N. Fournier} and \textit{S. Mischler}, J. Math. Pures Appl. (9) 84, No. 9, 1173--1234 (2005; Zbl 1088.82021) Full Text: DOI Link
Ha, Seung-Yeal Nonlinear functionals of the Boltzmann equation and uniform stability estimates. (English) Zbl 1069.76048 J. Differ. Equations 215, No. 1, 178-205 (2005). MSC: 76P05 45K05 35F25 82C40 PDFBibTeX XMLCite \textit{S.-Y. Ha}, J. Differ. Equations 215, No. 1, 178--205 (2005; Zbl 1069.76048) Full Text: DOI
Rezakhanlou, Fraydoun Boltzmann-Grad limits for stochastic hard sphere models. (English) Zbl 1233.82028 Commun. Math. Phys. 248, No. 3, 553-637 (2004). MSC: 82C22 60K35 82C40 PDFBibTeX XMLCite \textit{F. Rezakhanlou}, Commun. Math. Phys. 248, No. 3, 553--637 (2004; Zbl 1233.82028) Full Text: DOI
Mouhot, Clément; Villani, Cédric Regularity theory for the spatially homogeneous Boltzmann equation with cut-off. (English) Zbl 1063.76086 Arch. Ration. Mech. Anal. 173, No. 2, 169-212 (2004). MSC: 76P05 45K05 PDFBibTeX XMLCite \textit{C. Mouhot} and \textit{C. Villani}, Arch. Ration. Mech. Anal. 173, No. 2, 169--212 (2004; Zbl 1063.76086) Full Text: DOI arXiv
Golse, François; Saint-Raymond, Laure The Navier-Stokes limit of the Boltzmann equation for bounded collision kernels. (English) Zbl 1060.76101 Invent. Math. 155, No. 1, 81-161 (2004). Reviewer: Reinhard Illner (Victoria) MSC: 76P05 76D05 76A02 35F20 35Q30 76D03 82C40 PDFBibTeX XMLCite \textit{F. Golse} and \textit{L. Saint-Raymond}, Invent. Math. 155, No. 1, 81--161 (2004; Zbl 1060.76101) Full Text: DOI
Perthame, Benoît Mathematical tools for kinetic equations. (English) Zbl 1151.82351 Bull. Am. Math. Soc., New Ser. 41, No. 2, 205-244 (2004). Reviewer: Messoud A. Efendiev (Berlin) MSC: 82B40 76P05 35F10 PDFBibTeX XMLCite \textit{B. Perthame}, Bull. Am. Math. Soc., New Ser. 41, No. 2, 205--244 (2004; Zbl 1151.82351) Full Text: DOI
Laurençot, Philippe; Mischler, Stéphane Convergence to equilibrium for the continuous coagulation-fragmentation equation. (English) Zbl 1027.82030 Bull. Sci. Math. 127, No. 3, 179-190 (2003). MSC: 82C21 37L45 45M05 45G10 PDFBibTeX XMLCite \textit{P. Laurençot} and \textit{S. Mischler}, Bull. Sci. Math. 127, No. 3, 179--190 (2003; Zbl 1027.82030) Full Text: DOI
Rendall, Alan D. Theorems on existence and global dynamics for the Einstein equations. (English) Zbl 1024.83009 Living Rev. Relativ. 5, Article No. 2002-6, 62 p. (2002). MSC: 83C22 83C05 83-02 35Q75 PDFBibTeX XMLCite \textit{A. D. Rendall}, Living Rev. Relativ. 5, Article No. 2002--6, 62 p. (2002; Zbl 1024.83009) Full Text: DOI arXiv Link
Alexandre, R.; Villani, C. On the Boltzmann equation for long-range interactions. (English) Zbl 1029.82036 Commun. Pure Appl. Math. 55, No. 1, 30-70 (2002). Reviewer: A.Balint (Timişoara) MSC: 82C40 35F20 49J20 PDFBibTeX XMLCite \textit{R. Alexandre} and \textit{C. Villani}, Commun. Pure Appl. Math. 55, No. 1, 30--70 (2002; Zbl 1029.82036) Full Text: DOI
Aoki, Kazuo; Bardos, Claude; Dogbe, Christian; Golse, François A note on the propagation of boundary induced discontinuities in kinetic theory. (English) Zbl 1012.82014 Math. Models Methods Appl. Sci. 11, No. 9, 1581-1595 (2001). MSC: 82C40 76P05 PDFBibTeX XMLCite \textit{K. Aoki} et al., Math. Models Methods Appl. Sci. 11, No. 9, 1581--1595 (2001; Zbl 1012.82014) Full Text: DOI
Nouri, Anne Stationary states of a gas in a radiation field from a kinetic point of view. (English) Zbl 1006.82026 Ann. Fac. Sci. Toulouse, VI. Sér., Math. 10, No. 2, 361-390 (2001). Reviewer: Oleg A.Sinkevich (Moskva) MSC: 82C40 82D05 85A25 PDFBibTeX XMLCite \textit{A. Nouri}, Ann. Fac. Sci. Toulouse, Math. (6) 10, No. 2, 361--390 (2001; Zbl 1006.82026) Full Text: DOI Numdam EuDML Link
Escobedo, Miguel; Mischler, Stephane On a quantum Boltzmann equation for a gas of photons. (English) Zbl 1134.82318 J. Math. Pures Appl. (9) 80, No. 5, 471-515 (2001). Reviewer: Cornelis van der Mee (Arlington) MSC: 82C10 35Q40 82C40 PDFBibTeX XMLCite \textit{M. Escobedo} and \textit{S. Mischler}, J. Math. Pures Appl. (9) 80, No. 5, 471--515 (2001; Zbl 1134.82318) Full Text: DOI
Mieussens, L. Convergence of a discrete-velocity model for the Boltzmann-BGK equation. (English) Zbl 0980.82027 Comput. Math. Appl. 41, No. 1-2, 83-96 (2001). MSC: 82C40 65M12 PDFBibTeX XMLCite \textit{L. Mieussens}, Comput. Math. Appl. 41, No. 1--2, 83--96 (2001; Zbl 0980.82027) Full Text: DOI
Desvillettes, L.; Villani, C. On the trend to global equilibrium in spatially inhomogeneous entropy-dissipating systems: The linear Fokker-Planck equation. (English) Zbl 1029.82032 Commun. Pure Appl. Math. 54, No. 1, 1-42 (2001). Reviewer: Dirk Blömker (Aachen) MSC: 82C40 35Q99 46E99 47N55 60H99 60J99 82C70 PDFBibTeX XMLCite \textit{L. Desvillettes} and \textit{C. Villani}, Commun. Pure Appl. Math. 54, No. 1, 1--42 (2001; Zbl 1029.82032) Full Text: DOI
Arkeryd, Leif; Nouri, Anne \(L^1\) solutions to the stationary Boltzmann equation in a slab. (English) Zbl 0991.45005 Ann. Fac. Sci. Toulouse, VI. Sér., Math. 9, No. 3, 375-413 (2000). MSC: 45K05 82C40 PDFBibTeX XMLCite \textit{L. Arkeryd} and \textit{A. Nouri}, Ann. Fac. Sci. Toulouse, Math. (6) 9, No. 3, 375--413 (2000; Zbl 0991.45005) Full Text: DOI Numdam EuDML
Rendall, Alan D. Local and global existence theorems for the Einstein equations. (English) Zbl 0944.83002 Living Rev. Relativ. 3, Article No. 2000-1, no pag. (2000). MSC: 83-02 83C15 83C05 83A05 83C75 PDFBibTeX XMLCite \textit{A. D. Rendall}, Living Rev. Relativ. 3, Article No. 2000--1, no pag. (2000; Zbl 0944.83002) Full Text: DOI Link
Villani, C. Fisher information estimates for Boltzmann’s collision operator. (English) Zbl 0918.60093 J. Math. Pures Appl., IX. Sér. 77, No. 8, 821-837 (1998). MSC: 60K40 60H99 94A15 PDFBibTeX XMLCite \textit{C. Villani}, J. Math. Pures Appl. (9) 77, No. 8, 821--837 (1998; Zbl 0918.60093) Full Text: DOI
Lu, Xuguang A direct method for the regularity of the gain term in the Boltzmann equation. (English) Zbl 0913.76081 J. Math. Anal. Appl. 228, No. 2, 409-435 (1998). MSC: 76P05 45K05 PDFBibTeX XMLCite \textit{X. Lu}, J. Math. Anal. Appl. 228, No. 2, 409--435 (1998; Zbl 0913.76081) Full Text: DOI
Cercignani, C. Existence and trend to equilibrium of weak solutions of the Boltzmann equation. (English) Zbl 0907.35100 Nonlinear Anal., Theory Methods Appl. 30, No. 6, 3749-3761 (1997). Reviewer: L.Debnath (Orlando) MSC: 35Q35 76P05 35D05 PDFBibTeX XMLCite \textit{C. Cercignani}, Nonlinear Anal., Theory Methods Appl. 30, No. 6, 3749--3761 (1997; Zbl 0907.35100) Full Text: DOI
Arkeryd, l.; Nouri, A. Boltzmann asymptotics with diffuse reflection boundary conditions. (English) Zbl 0877.76063 Monatsh. Math. 123, No. 4, 285-298 (1997). Reviewer: J.Mawhin (Louvain-La-Neuve) MSC: 76P05 82B40 45K05 PDFBibTeX XMLCite \textit{l. Arkeryd} and \textit{A. Nouri}, Monatsh. Math. 123, No. 4, 285--298 (1997; Zbl 0877.76063) Full Text: DOI EuDML
Desvillettes, Laurent Regularization for the non-cutoff 2D radially symmetric Boltzmann equation with a velocity dependent cross section. (English) Zbl 0871.76077 Transp. Theory Stat. Phys. 25, No. 3-5, 383-394 (1996). MSC: 76P05 PDFBibTeX XMLCite \textit{L. Desvillettes}, Transp. Theory Stat. Phys. 25, No. 3--5, 383--394 (1996; Zbl 0871.76077) Full Text: DOI
Cercignani, C. Trend to equilibrium of weak solutions of the Boltzmann equation in a slab with diffusive boundary conditions. (English) Zbl 1081.82614 J. Stat. Phys. 84, No. 3-4, 875-888 (1996). MSC: 82C40 45K05 76P05 PDFBibTeX XMLCite \textit{C. Cercignani}, J. Stat. Phys. 84, No. 3--4, 875--888 (1996; Zbl 1081.82614) Full Text: DOI
Bellomo, N.; LeTallec, P.; Perthame, B. The solution of the nonlinear Boltzmann equation: A survey of analytic and computational methods. (English) Zbl 0832.76084 Comput. Math. Appl. 30, No. 7, 21-30 (1995). MSC: 76P05 76-02 45K05 PDFBibTeX XMLCite \textit{N. Bellomo} et al., Comput. Math. Appl. 30, No. 7, 21--30 (1995; Zbl 0832.76084) Full Text: DOI
Desvillettes, Laurent About the regularizing properties of the non-cut-off Kac equation. (English) Zbl 0827.76081 Commun. Math. Phys. 168, No. 2, 417-440 (1995). MSC: 76P05 82D05 PDFBibTeX XMLCite \textit{L. Desvillettes}, Commun. Math. Phys. 168, No. 2, 417--440 (1995; Zbl 0827.76081) Full Text: DOI
Lions, Pierre Louis On the existence and convergence of solutions of Boltzmann equations. (English) Zbl 0813.45003 Rend. Semin. Mat. Fis. Milano 62, 115-125 (1992). Reviewer: T.Aktosun (Fargo) MSC: 45K05 82C40 76P05 PDFBibTeX XMLCite \textit{P. L. Lions}, Rend. Semin. Mat. Fis. Milano 62, 115--125 (1992; Zbl 0813.45003) Full Text: DOI