Refined blow-up criteria for the full compressible Navier-Stokes equations involving temperature

被引：8

作者：

Jiu, Quansen ^{[1
]}

Wang, Yanqing ^{[2
]}

Ye, Yulin ^{[3
]}

机构：

[1] Capital Normal Univ, Sch Math Sci, Beijing 100048, Peoples R China

[2] Zhengzhou Univ Light Ind, Dept Math & Informat Sci, Zhengzhou 450002, Henan, Peoples R China

[3] Henan Univ, Sch Math & Stat, Kaifeng 475004, Peoples R China

来源：

JOURNAL OF EVOLUTION EQUATIONS | 2021年 / 21卷 / 02期

基金：

中国博士后科学基金; 中国国家自然科学基金; 北京市自然科学基金;

关键词：

Full compressible Navier-Stokes equations; Strong solutions; Blow-up criteria; SUITABLE WEAK SOLUTIONS; REGULARITY CRITERIA; INTERIOR REGULARITY; CLASSICAL-SOLUTIONS; SMOOTH SOLUTIONS; EXISTENCE; PRESSURE; VACUUM;

D O I：

10.1007/s00028-020-00660-4

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper, inspired by the study of the energy flux in local energy inequality of the 3D incompressible Navier-Stokes equations, we improve almost all the blow-up criteria involving temperature to allow the temperature in its scaling invariant space for the 3D full compressible Navier-Stokes equations. Enlightening regular criteria via pressure Pi = divdiv/-Delta (u(i) u(j)) of the 3D incompressible Navier-Stokes equations on bounded domain, we generalize Beirao da Veiga's result in (Chin Ann Math Ser B 16:407-412, 1995) from the incompressible Navier-Stokes equations to the isentropic compressible Navier-Stokes system in the case away from vacuum.

引用

页码：1895 / 1916

页数：22

共 44 条

[1] Regularity criteria involving the pressure for the weak solutions to the Navier-Stokes equations
Berselli, LC
Galdi, GP
[J]. PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 2002, 130 (12) : 3585 - 3595
[2] PARTIAL REGULARITY OF SUITABLE WEAK SOLUTIONS OF THE NAVIER-STOKES EQUATIONS
CAFFARELLI, L
KOHN, R
NIRENBERG, L
[J]. COMMUNICATIONS ON PURE AND APPLIED MATHEMATICS, 1982, 35 (06) : 771 - 831
[3] On the interior regularity of suitable weak solutions to the Navier-Stokes equations
Chae, Dongho
Kang, Kyungkeun
Lee, Jihoon
[J]. COMMUNICATIONS IN PARTIAL DIFFERENTIAL EQUATIONS, 2007, 32 (7-9) : 1189 - 1207
[4] Unique solvability of the initial boundary value problems for compressible viscous fluids
Cho, Y
Choe, HJ
Kim, H
[J]. JOURNAL DE MATHEMATIQUES PURES ET APPLIQUEES, 2004, 83 (02): : 243 - 275
[5] Existence results for viscous polytropic fluids with vacuum
Cho, Yonggeun
Kim, Hyunseok
[J]. JOURNAL OF DIFFERENTIAL EQUATIONS, 2006, 228 (02) : 377 - 411
[6] Blow up criteria for the compressible Navier-Stokes equations
Choe, Hi Jun
Yang, Minsuk
[J]. MATHEMATICAL ANALYSIS IN FLUID MECHANICS: SELECTED RECENT RESULTS, 2018, 710 : 65 - 84
[7] daVeiga HB, 1995, CHINESE ANN MATH B, V16, P407
[8] BLOWUP CRITERION FOR 3-DIMENSIONAL COMPRESSIBLE NAVIER-STOKES EQUATIONS INVOLVING VELOCITY DIVERGENCE
Du, Lili
Wang, Yongfu
[J]. COMMUNICATIONS IN MATHEMATICAL SCIENCES, 2014, 12 (08) : 1427 - 1435
[9] Blow-up criteria for the Navier-Stokes equations of compressible fluids
Fan, Jishan
Jiang, Song
[J]. JOURNAL OF HYPERBOLIC DIFFERENTIAL EQUATIONS, 2008, 5 (01) : 167 - 185
[10] A blow-up criterion for compressible viscous heat-conductive flows
Fan, Jishan
Jiang, Song
Ou, Yaobin
[J]. ANNALES DE L INSTITUT HENRI POINCARE-ANALYSE NON LINEAIRE, 2010, 27 (01): : 337 - 350

← 1 2 3 4 5 →