Ramani, Raaghav; Reisner, Jon; Shkoller, Steve A space-time smooth artificial viscosity method with wavelet noise indicator and shock collision scheme. I: The 1-\(D\) case. (English) Zbl 1452.76159 J. Comput. Phys. 387, 81-116 (2019). MSC: 76M20 76N15 76L05 65M06 65T60 65Z05 PDF BibTeX XML Cite \textit{R. Ramani} et al., J. Comput. Phys. 387, 81--116 (2019; Zbl 1452.76159) Full Text: DOI arXiv OpenURL
Ramani, Raaghav; Reisner, Jon; Shkoller, Steve A space-time smooth artificial viscosity method with wavelet noise indicator and shock collision scheme. II: The 2-\(D\) case. (English) Zbl 1452.76158 J. Comput. Phys. 387, 45-80 (2019). MSC: 76M20 76N15 76L05 65M06 65T60 65Z05 PDF BibTeX XML Cite \textit{R. Ramani} et al., J. Comput. Phys. 387, 45--80 (2019; Zbl 1452.76158) Full Text: DOI arXiv OpenURL
Shkoller, Steve; Sideris, Thomas C. Global existence of near-affine solutions to the compressible Euler equations. (English) Zbl 1445.76063 Arch. Ration. Mech. Anal. 234, No. 1, 115-180 (2019). MSC: 76N10 35Q31 PDF BibTeX XML Cite \textit{S. Shkoller} and \textit{T. C. Sideris}, Arch. Ration. Mech. Anal. 234, No. 1, 115--180 (2019; Zbl 1445.76063) Full Text: DOI arXiv OpenURL
Hadžić, Mahir; Shkoller, Steve; Speck, Jared A priori estimates for solutions to the relativistic Euler equations with a moving vacuum boundary. (English) Zbl 1420.35211 Commun. Partial Differ. Equations 44, No. 10, 859-906 (2019). MSC: 35Q31 35B45 76Y05 83A05 PDF BibTeX XML Cite \textit{M. Hadžić} et al., Commun. Partial Differ. Equations 44, No. 10, 859--906 (2019; Zbl 1420.35211) Full Text: DOI arXiv Link OpenURL
Coutand, Daniel; Shkoller, Steve Regularity of the velocity field for Euler vortex patch evolution. (English) Zbl 1384.35071 Trans. Am. Math. Soc. 370, No. 5, 3689-3720 (2018). MSC: 35Q31 35B65 76B47 76B03 PDF BibTeX XML Cite \textit{D. Coutand} and \textit{S. Shkoller}, Trans. Am. Math. Soc. 370, No. 5, 3689--3720 (2018; Zbl 1384.35071) Full Text: DOI arXiv OpenURL
Coutand, Daniel; Shkoller, Steve On the impossibility of finite-time splash singularities for vortex sheets. (English) Zbl 1338.35343 Arch. Ration. Mech. Anal. 221, No. 2, 987-1033 (2016). MSC: 35Q31 35B44 PDF BibTeX XML Cite \textit{D. Coutand} and \textit{S. Shkoller}, Arch. Ration. Mech. Anal. 221, No. 2, 987--1033 (2016; Zbl 1338.35343) Full Text: DOI arXiv Link OpenURL
Coutand, Daniel; Shkoller, Steve On the finite-time splash and splat singularities for the 3-D free-surface Euler equations. (English) Zbl 1285.35071 Commun. Math. Phys. 325, No. 1, 143-183 (2014). Reviewer: Thomas Ernst (Uppsala) MSC: 35Q31 PDF BibTeX XML Cite \textit{D. Coutand} and \textit{S. Shkoller}, Commun. Math. Phys. 325, No. 1, 143--183 (2014; Zbl 1285.35071) Full Text: DOI arXiv OpenURL
Coutand, Daniel; Hole, Jason; Shkoller, Steve Well-posedness of the free-boundary compressible 3-D Euler equations with surface tension and the zero surface tension limit. (English) Zbl 1297.35181 SIAM J. Math. Anal. 45, No. 6, 3690-3767 (2013). Reviewer: Galina Bizhanova (Almaty) MSC: 35Q35 35R35 35L70 35B20 76B03 PDF BibTeX XML Cite \textit{D. Coutand} et al., SIAM J. Math. Anal. 45, No. 6, 3690--3767 (2013; Zbl 1297.35181) Full Text: DOI arXiv OpenURL
Coutand, Daniel; Shkoller, Steve Well-posedness in smooth function spaces for the moving-boundary three-dimensional compressible Euler equations in physical vacuum. (English) Zbl 1257.35147 Arch. Ration. Mech. Anal. 206, No. 2, 515-616 (2012). MSC: 35Q31 35R37 35R35 35D40 PDF BibTeX XML Cite \textit{D. Coutand} and \textit{S. Shkoller}, Arch. Ration. Mech. Anal. 206, No. 2, 515--616 (2012; Zbl 1257.35147) Full Text: DOI arXiv Link OpenURL
Coutand, Daniel; Shkoller, Steve Well-posedness in smooth function spaces for moving-boundary 1-D compressible Euler equations in physical vacuum. (English) Zbl 1217.35119 Commun. Pure Appl. Math. 64, No. 3, 328-366 (2011). Reviewer: Titus Petrila (Cluj-Napoca) MSC: 35L65 76E19 35Q31 35R37 PDF BibTeX XML Cite \textit{D. Coutand} and \textit{S. Shkoller}, Commun. Pure Appl. Math. 64, No. 3, 328--366 (2011; Zbl 1217.35119) Full Text: DOI arXiv Link OpenURL
Coutand, Daniel; Shkoller, Steve A simple proof of well-posedness for the free-surface incompressible Euler equations. (English) Zbl 1210.35163 Discrete Contin. Dyn. Syst., Ser. S 3, No. 3, 429-449 (2010). MSC: 35L65 35L70 35L80 35Q35 35R35 76B03 PDF BibTeX XML Cite \textit{D. Coutand} and \textit{S. Shkoller}, Discrete Contin. Dyn. Syst., Ser. S 3, No. 3, 429--449 (2010; Zbl 1210.35163) Full Text: DOI OpenURL
Cheng, C. H. Arthur; Coutand, Daniel; Shkoller, Steve On the limit as the density ratio tends to zero for two perfect incompressible fluids separated by a surface of discontinuity. (English) Zbl 1247.35100 Commun. Partial Differ. Equations 35, No. 5, 817-845 (2010). Reviewer: Oleg Titow (Berlin) MSC: 35Q35 76B03 35R35 76T10 76B45 PDF BibTeX XML Cite \textit{C. H. A. Cheng} et al., Commun. Partial Differ. Equations 35, No. 5, 817--845 (2010; Zbl 1247.35100) Full Text: DOI Link OpenURL
Coutand, Daniel; Lindblad, Hans; Shkoller, Steve A priori estimates for the free-boundary 3D compressible Euler equations in physical vacuum. (English) Zbl 1193.35139 Commun. Math. Phys. 296, No. 2, 559-587 (2010). MSC: 35Q31 35B45 35R37 76N10 PDF BibTeX XML Cite \textit{D. Coutand} et al., Commun. Math. Phys. 296, No. 2, 559--587 (2010; Zbl 1193.35139) Full Text: DOI arXiv OpenURL
Cheng, Ching-Hsiao Arthur; Shkoller, Steve; Coutand, Daniel On the motion of vortex sheets with surface tension in three-dimensional Euler equations with vorticity. (English) Zbl 1165.35041 Commun. Pure Appl. Math. 61, No. 12, 1715-1752 (2008). Reviewer: Valery V. Karachik (Chelyabinsk) MSC: 35Q35 76B03 35B45 PDF BibTeX XML Cite \textit{C.-H. A. Cheng} et al., Commun. Pure Appl. Math. 61, No. 12, 1715--1752 (2008; Zbl 1165.35041) Full Text: DOI OpenURL
Coutand, Daniel; Shkoller, Steve Well-posedness of the free-surface incompressible Euler equations with or without surface tension. (English) Zbl 1123.35038 J. Am. Math. Soc. 20, No. 3, 829-930 (2007). Reviewer: Georg V. Jaiani (Tbilisi) MSC: 35Q05 76B03 35Q35 35R35 PDF BibTeX XML Cite \textit{D. Coutand} and \textit{S. Shkoller}, J. Am. Math. Soc. 20, No. 3, 829--930 (2007; Zbl 1123.35038) Full Text: DOI arXiv OpenURL
Marsden, Jerrold E.; Shkoller, Steve The anisotropic Lagrangian averaged Euler and Navier-Stokes equations. (English) Zbl 1020.76014 Arch. Ration. Mech. Anal. 166, No. 1, 27-46 (2003). Reviewer: Isabell Gallagher (Palaiseau) MSC: 76D03 76B03 35Q30 35Q35 PDF BibTeX XML Cite \textit{J. E. Marsden} and \textit{S. Shkoller}, Arch. Ration. Mech. Anal. 166, No. 1, 27--46 (2003; Zbl 1020.76014) Full Text: DOI arXiv Link OpenURL
Marsden, Jerrold E.; Shkoller, Steve Global well-posedness for the Lagrangian averaged Navier-Stokes (LANS-\(\alpha\)) equations on bounded domains. (English) Zbl 1006.35074 Philos. Trans. R. Soc. Lond., Ser. A, Math. Phys. Eng. Sci. 359, No. 1784, 1449-1468 (2001). Reviewer: Il’ya Sh.Mogilevskij (Tver) MSC: 35Q30 76D03 35Q05 PDF BibTeX XML Cite \textit{J. E. Marsden} and \textit{S. Shkoller}, Philos. Trans. R. Soc. Lond., Ser. A, Math. Phys. Eng. Sci. 359, No. 1784, 1449--1468 (2001; Zbl 1006.35074) Full Text: DOI Link OpenURL
Oliver, Marcel; Shkoller, Steve The vortex blob method as a second-grade non-Newtonian fluid. (English) Zbl 0983.35106 Commun. Partial Differ. Equations 26, No. 1-2, 295-314 (2001). Reviewer: Qin Mengzhao (Beijing) MSC: 35Q35 76A05 35Q05 PDF BibTeX XML Cite \textit{M. Oliver} and \textit{S. Shkoller}, Commun. Partial Differ. Equations 26, No. 1--2, 295--314 (2001; Zbl 0983.35106) Full Text: DOI arXiv OpenURL
Shkoller, S. Smooth global Lagrangian flow for the 2D Euler and second-grade fluid equations. (English) Zbl 0982.58024 Appl. Math. Lett. 14, No. 5, 539-543 (2001). Reviewer: Messoud Efendiev (Berlin) MSC: 58J90 76A05 35Q35 35B65 PDF BibTeX XML Cite \textit{S. Shkoller}, Appl. Math. Lett. 14, No. 5, 539--543 (2001; Zbl 0982.58024) Full Text: DOI arXiv OpenURL
Shkoller, Steve Analysis on groups of diffeomorphisms of manifolds with boundary and the averaged motion of a fluid. (English) Zbl 1044.35061 J. Differ. Geom. 55, No. 1, 145-191 (2000). Reviewer: Jan Chrastina (Brno) MSC: 35Q35 35A30 58D05 58J32 37K65 76D05 76F20 PDF BibTeX XML Cite \textit{S. Shkoller}, J. Differ. Geom. 55, No. 1, 145--191 (2000; Zbl 1044.35061) Full Text: DOI OpenURL
Marsden, Jerrold E.; Pekarsky, Sergey; Shkoller, Steve Poisson structure and invariant manifolds on Lie groups. (English) Zbl 0963.65129 Fiedler, B. (ed.) et al., International conference on differential equations. Proceedings of the conference, Equadiff ’99, Berlin, Germany, August 1-7, 1999. Vol. 2. Singapore: World Scientific. 1192-1197 (2000). MSC: 65P10 37M15 37J15 PDF BibTeX XML Cite \textit{J. E. Marsden} et al., in: International conference on differential equations. Proceedings of the conference, Equadiff '99, Berlin, Germany, August 1--7, 1999. Vol. 2. Singapore: World Scientific. 1192--1197 (2000; Zbl 0963.65129) OpenURL
Marsden, Jerrold E.; Pekarsky, Sergey; Shkoller, Steve Symmetry reduction of discrete Lagrangian mechanics on Lie groups. (English) Zbl 0976.70011 J. Geom. Phys. 36, No. 1-2, 140-151 (2000). MSC: 70G65 70G45 70H03 70H33 70E15 PDF BibTeX XML Cite \textit{J. E. Marsden} et al., J. Geom. Phys. 36, No. 1--2, 140--151 (2000; Zbl 0976.70011) Full Text: DOI arXiv OpenURL
Marsden, J. E.; Ratiu, T. S.; Shkoller, S. The geometry and analysis of the averaged Euler equations and a new diffeomorphism group. (English) Zbl 0979.58004 Geom. Funct. Anal. 10, No. 3, 582-599 (2000). Reviewer: Nicolai Konstantinovish Smolentsev (Kemerovo) MSC: 58D05 58D30 76D05 PDF BibTeX XML Cite \textit{J. E. Marsden} et al., Geom. Funct. Anal. 10, No. 3, 582--599 (2000; Zbl 0979.58004) Full Text: DOI arXiv OpenURL
Castrillón López, Marco; Ratiu, Tudor S.; Shkoller, Steve Reduction in principal fiber bundles: Covariant Euler-Poincaré equations. (English) Zbl 0967.53019 Proc. Am. Math. Soc. 128, No. 7, 2155-2164 (2000). Reviewer: A.D.Osborne (Keele) MSC: 53C05 53C10 PDF BibTeX XML Cite \textit{M. Castrillón López} et al., Proc. Am. Math. Soc. 128, No. 7, 2155--2164 (2000; Zbl 0967.53019) Full Text: DOI arXiv OpenURL
Marsden, Jerrold E.; Pekarsky, Sergey; Shkoller, Steve Discrete Euler-Poincaré and Lie-Poisson equations. (English) Zbl 0978.37045 Nonlinearity 12, No. 6, 1647-1662 (1999). Reviewer: Marco Modugno (Firenze) MSC: 37J15 53D20 70H33 70E15 PDF BibTeX XML Cite \textit{J. E. Marsden} et al., Nonlinearity 12, No. 6, 1647--1662 (1999; Zbl 0978.37045) Full Text: DOI arXiv Link OpenURL