Blow-up criterion for the 3D compressible non-isentropic Navier–Stokes equations without thermal conductivity
Tài liệu tham khảo
Agmon, 1959, Estimates near the boundary for solutions of elliptic partial differential equations satisfying general boundary conditions. I, Comm. Pure Appl. Math., 12, 623, 10.1002/cpa.3160120405
Beale, 1984, Remarks on the breakdown of smooth solutions for the 3D Euler equations, Comm. Math. Phys., 94, 61, 10.1007/BF01212349
Cho, 2006, Existence results for viscous polytropic fluids with vacuum, J. Differential Equations, 228, 377, 10.1016/j.jde.2006.05.001
Galdi, 1994
Hoff, 1995, Global solutions of the Navier–Stokes equations for multidimensional compressible flow with discontinuous initial data, J. Differential Equations, 120, 215, 10.1006/jdeq.1995.1111
Huang, 2011, Blow-up criterion for viscous barotropic flows with vacuum states, Comm. Math. Phys., 301, 23, 10.1007/s00220-010-1148-y
Huang, 2011, Serrin-type criterion for the three-dimensional viscous compressible flows, SIAM J. Math. Anal., 43, 1872, 10.1137/100814639
Huang, 2012, Global well-posedness of classical solutions with large oscillations and vacuum to the three-dimensional isentropic compressible Navier–Stokes equations, Comm. Pure Appl. Math., 65, 549, 10.1002/cpa.21382
X. Huang, J. Li, Z. Xin, Global well-posedness for classical solutions to the multi-dimensional isentropic compressible Navier–Stokes system with vacuum on bounded domains, preprint, 2012.
Ladyzenskaja, 1968
Ponce, 1985, Remarks on a paper: “Remarks on the breakdown of smooth solutions for the 3D Euler equations”, Comm. Math. Phys., 98, 349, 10.1007/BF01205787
Sun, 2011, A Beale–Kato–Majda blow-up criterion to the compressible Navier–Stokes equation, J. Math. Pures Appl., 95, 36, 10.1016/j.matpur.2010.08.001
Wen, 2013, Blow-up criterions of strong solutions to 3D compressible Navier–Stokes equations with vacuum, Adv. Math., 248, 534, 10.1016/j.aim.2013.07.018
Xin, 1998, Blow-up of smooth solutions to the compressible Navier–Stokes equations with compact density, Comm. Pure Appl. Math., 51, 0229, 10.1002/(SICI)1097-0312(199803)51:3<229::AID-CPA1>3.0.CO;2-C
Xin, 2013, On blow-up of classical solutions to the compressible Navier–Stokes equations, Comm. Math. Phys., 321, 529, 10.1007/s00220-012-1610-0