Kawashima, Shuichi; Shibata, Yoshihiro; Xu, Jiang Dissipative structure for symmetric hyperbolic-parabolic systems with Korteweg-type dispersion. (English) Zbl 07481876 Commun. Partial Differ. Equations 47, No. 2, 378-400 (2022). MSC: 35G50 35B40 35Q35 35Q53 PDF BibTeX XML Cite \textit{S. Kawashima} et al., Commun. Partial Differ. Equations 47, No. 2, 378--400 (2022; Zbl 07481876) Full Text: DOI OpenURL
Xu, Jiang; Kawashima, Shuichi The frequency-localization technique and minimal decay-regularity for Euler-Maxwell equations. (English) Zbl 1356.35250 J. Math. Anal. Appl. 446, No. 2, 1537-1554 (2017). MSC: 35Q82 82D10 35Q60 76X05 78A25 35B65 PDF BibTeX XML Cite \textit{J. Xu} and \textit{S. Kawashima}, J. Math. Anal. Appl. 446, No. 2, 1537--1554 (2017; Zbl 1356.35250) Full Text: DOI arXiv OpenURL
Xu, Jiang; Kawashima, Shuichi The minimal decay regularity of smooth solutions to the Euler-Maxwell two-fluid system. (English) Zbl 1359.35160 J. Hyperbolic Differ. Equ. 13, No. 4, 719-733 (2016). MSC: 35Q35 35B40 35L45 82D10 76X05 35B65 76N10 78A25 35Q61 PDF BibTeX XML Cite \textit{J. Xu} and \textit{S. Kawashima}, J. Hyperbolic Differ. Equ. 13, No. 4, 719--733 (2016; Zbl 1359.35160) Full Text: DOI OpenURL
Ueda, Yoshihiro; Kawashima, Shuichi Stability of stationary solutions for the non-isentropic Euler-Maxwell system in the whole space. (English) Zbl 1356.35042 Bull. Braz. Math. Soc. (N.S.) 47, No. 2, 787-797 (2016). MSC: 35B35 35B40 35L40 35Q31 35B45 35Q61 PDF BibTeX XML Cite \textit{Y. Ueda} and \textit{S. Kawashima}, Bull. Braz. Math. Soc. (N.S.) 47, No. 2, 787--797 (2016; Zbl 1356.35042) Full Text: DOI OpenURL
Xu, Jiang; Kawashima, Shuichi Frequency-localization Duhamel principle and its application to the optimal decay of dissipative systems in low dimensions. (English) Zbl 1347.35043 J. Differ. Equations 261, No. 5, 2670-2701 (2016). MSC: 35B40 35L60 35L45 35F25 35L65 PDF BibTeX XML Cite \textit{J. Xu} and \textit{S. Kawashima}, J. Differ. Equations 261, No. 5, 2670--2701 (2016; Zbl 1347.35043) Full Text: DOI OpenURL
Kawashima, Shuichi; Ueda, Yoshihiro Mathematical entropy and Euler-Cattaneo-Maxwell system. (English) Zbl 1336.35226 Anal. Appl., Singap. 14, No. 1, 101-143 (2016). Reviewer: Ilya A. Chernov (Petrozavodsk) MSC: 35L60 76X05 35B35 35B40 35A01 35Q31 35Q61 PDF BibTeX XML Cite \textit{S. Kawashima} and \textit{Y. Ueda}, Anal. Appl., Singap. 14, No. 1, 101--143 (2016; Zbl 1336.35226) Full Text: DOI OpenURL
Xu, Jiang; Mori, Naofumi; Kawashima, Shuichi \(L^p - L^q - L^r\) estimates and minimal decay regularity for compressible Euler-Maxwell equations. (English. French summary) Zbl 1330.35052 J. Math. Pures Appl. (9) 104, No. 5, 965-981 (2015). Reviewer: Michael Reissig (Freiberg) MSC: 35B45 35B35 35L40 35B40 82D10 35Q31 35Q61 35A09 PDF BibTeX XML Cite \textit{J. Xu} et al., J. Math. Pures Appl. (9) 104, No. 5, 965--981 (2015; Zbl 1330.35052) Full Text: DOI arXiv OpenURL
Xu, Jiang; Kawashima, Shuichi The optimal decay estimates on the framework of Besov spaces for generally dissipative systems. (English) Zbl 1323.35141 Arch. Ration. Mech. Anal. 218, No. 1, 275-315 (2015). MSC: 35Q31 42B25 76N15 PDF BibTeX XML Cite \textit{J. Xu} and \textit{S. Kawashima}, Arch. Ration. Mech. Anal. 218, No. 1, 275--315 (2015; Zbl 1323.35141) Full Text: DOI arXiv OpenURL
Xu, Jiang; Kawashima, Shuichi Diffusive relaxation limit of classical solutions to the damped compressible Euler equations. (English) Zbl 1329.35238 J. Differ. Equations 256, No. 2, 771-796 (2014). Reviewer: Thomas Ernst (Uppsala) MSC: 35Q31 76N10 42B25 PDF BibTeX XML Cite \textit{J. Xu} and \textit{S. Kawashima}, J. Differ. Equations 256, No. 2, 771--796 (2014; Zbl 1329.35238) Full Text: DOI OpenURL
Feng, Yue-Hong; Wang, Shu; Kawashima, Shuichi Global existence and asymptotic decay of solutions to the non-isentropic Euler-Maxwell system. (English) Zbl 1304.35517 Math. Models Methods Appl. Sci. 24, No. 14, 2851 (2014). MSC: 35Q31 35A01 35L45 35L60 35Q35 35B65 35Q61 35B40 PDF BibTeX XML Cite \textit{Y.-H. Feng} et al., Math. Models Methods Appl. Sci. 24, No. 14, 2851 (2014; Zbl 1304.35517) Full Text: DOI arXiv OpenURL
Xu, Jiang; Kawashima, Shuichi Global classical solutions for partially dissipative hyperbolic system of balance laws. (English) Zbl 1293.35173 Arch. Ration. Mech. Anal. 211, No. 2, 513-553 (2014). MSC: 35L65 35B44 35B65 35Q31 PDF BibTeX XML Cite \textit{J. Xu} and \textit{S. Kawashima}, Arch. Ration. Mech. Anal. 211, No. 2, 513--553 (2014; Zbl 1293.35173) Full Text: DOI arXiv OpenURL
Xu, Jiang; Xiong, Jun; Kawashima, Shuichi Global well-posedness in critical Besov spaces for two-fluid Euler-Maxwell equations. (English) Zbl 1292.35243 SIAM J. Math. Anal. 45, No. 3, 1422-1447 (2013). Reviewer: Rainer Picard (Dresden) MSC: 35Q35 35Q31 76X05 PDF BibTeX XML Cite \textit{J. Xu} et al., SIAM J. Math. Anal. 45, No. 3, 1422--1447 (2013; Zbl 1292.35243) Full Text: DOI arXiv OpenURL
Ueda, Yoshihiro; Wang, Shu; Kawashima, Shuichi Dissipative structure of the regularity-loss type and time asymptotic decay of solutions for the Euler-Maxwell system. (English) Zbl 1252.35073 SIAM J. Math. Anal. 44, No. 3, 2002-2017 (2012). MSC: 35B40 35B35 35L40 82D10 35Q31 35Q61 PDF BibTeX XML Cite \textit{Y. Ueda} et al., SIAM J. Math. Anal. 44, No. 3, 2002--2017 (2012; Zbl 1252.35073) Full Text: DOI Link OpenURL
Kawashima, Shuichi; Ueda, Yoshihiro Decay property of regularity-loss type for the Euler-Maxwell system. (English) Zbl 1282.35069 Methods Appl. Anal. 18, No. 3, 245-268 (2011). MSC: 35B40 35B35 35L40 82D10 35Q31 35Q61 PDF BibTeX XML Cite \textit{S. Kawashima} and \textit{Y. Ueda}, Methods Appl. Anal. 18, No. 3, 245--268 (2011; Zbl 1282.35069) Full Text: DOI Link OpenURL
Makino, Tetu; Ukai, Seiji; Kawashima, Shuichi Sur la solution à support compact de l’equation d’Euler compressible. (Solutions with compact support of the compressible Euler equation). (French) Zbl 0637.76065 Japan J. Appl. Math. 3, 249-257 (1986). MSC: 76N10 35Q30 PDF BibTeX XML Cite \textit{T. Makino} et al., Japan J. Appl. Math. 3, 249--257 (1986; Zbl 0637.76065) Full Text: DOI OpenURL
Kawashima, Shuichi The asymptotic equivalence of the Broadwell model equation and its Navier-Stokes model equation. (English) Zbl 0477.76034 Jap. J. Math., New Ser. 7, 1-43 (1981). MSC: 76D05 PDF BibTeX XML Cite \textit{S. Kawashima}, Jpn. J. Math., New Ser. 7, 1--43 (1981; Zbl 0477.76034) OpenURL