GLOBAL STRONG SOLUTION TO THE MULTIDIMENSIONAL INHOMOGENEOUS INCOMPRESSIBLE HEAT CONDUCTING NAVIER-STOKES FLOWS WITH VACUUM

被引：0

作者：

Liu, Yang ^{[1
,2
]}

Zhou, Nan ^{[1
]}

Guo, Renying ^{[1
]}

机构：

[1] Changchun Normal Univ, Changchun, Peoples R China

[2] Jilin Univ, Sch Math, Changchun, Peoples R China

来源：

ROCKY MOUNTAIN JOURNAL OF MATHEMATICS | 2021年 / 51卷 / 04期

基金：

中国国家自然科学基金;

关键词：

inhomogeneous Navier-Stokes equations; heat conducting flows; global strong solutions; vacuum; EXISTENCE; EQUATIONS; DENSITY; FLUIDS;

D O I：

10.1216/rmj.2021.51.1315

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We are concerned with the Cauchy problem of the multidimensional inhomogeneous incompressible heat conducting Navier-Stokes flows with fractional dissipation. We show that the problem admits a unique global strong solution. Note that the initial data can be arbitrarily large and the initial density can contain vacuum states.

引用

页码：1315 / 1328

页数：14

共 15 条

[1] [Anonymous], 1996, OXFORD LECT SERIES M
[2] Antontsev S.N., 1990, STUDIES MATH ITS APP, V22
[3] Maximizers for Gagliardo-Nirenberg inequalities and related non-local problems
Bellazzini, Jacopo
Frank, Rupert L.
Visciglia, Nicola
[J]. MATHEMATISCHE ANNALEN, 2014, 360 (3-4) : 653 - 673
[4] Existence result for heat-conducting viscous incompressible fluids with vacuum
Cho, Yonggeun
Kim, Hyunseok
[J]. JOURNAL OF THE KOREAN MATHEMATICAL SOCIETY, 2008, 45 (03) : 645 - 681
[5] Strong solutions of the Navier-Stokes equations for nonhomogeneous incompressible fluids
Choe, HJ
Kim, H
[J]. COMMUNICATIONS IN PARTIAL DIFFERENTIAL EQUATIONS, 2003, 28 (5-6) : 1183 - 1201
[6] Global Wellposedness for the 3D Inhomogeneous Incompressible Navier-Stokes Equations
Craig, Walter
Huang, Xiangdi
Wang, Yun
[J]. JOURNAL OF MATHEMATICAL FLUID MECHANICS, 2013, 15 (04) : 747 - 758
[7] He C., 2017, 170905608 ARXIV 170905608 ARXIV
[8] Global strong solution to the 2D nonhomogeneous incompressible MHD system
Huang, Xiangdi
Wang, Yun
[J]. JOURNAL OF DIFFERENTIAL EQUATIONS, 2013, 254 (02) : 511 - 527
[9] KAZHIKHO.AV, 1974, DOKL AKAD NAUK SSSR+, V216, P1008
[10] Global existence and large time asymptotic behavior of strong solutions to the Cauchy problem of 2D density-dependent Navier-Stokes equations with vacuum
Lu, Boqiang
Shi, Xiaoding
Zhong, Xin
[J]. NONLINEARITY, 2018, 31 (06) : 2617 - 2632

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