Regularity of Weak Solutions to the Inhomogeneous Stationary Navier-Stokes Equations

被引：1
作者：
Tartaglione, Alfonsina [1 ]
机构：
[1] Univ Campania Luigi Vanvitelli, Dipartimento Matemat & Fis, I-81100 Caserta, Italy
来源：
SYMMETRY-BASEL | 2021年 / 13卷 / 08期
关键词：
stationary Navier-Stokes equations; weak solutions; regularity; PRESSURE; FLUIDS; FLOWS;
D O I：
10.3390/sym13081336
中图分类号：
O [数理科学和化学]; P [天文学、地球科学]; Q [生物科学]; N [自然科学总论];
学科分类号：
07 ; 0710 ; 09 ;
摘要：
One of the most intriguing issues in the mathematical theory of the stationary Navier-Stokes equations is the regularity of weak solutions. This problem has been deeply investigated for homogeneous fluids. In this paper, the regularity of the solutions in the case of not constant viscosity is analyzed. Precisely, it is proved that for a bounded domain Omega subset of R-2, a weak solution u is an element of W-1,W-q(Omega) is locally Holder continuous if q=2, and Holder continuous around x, if q is an element of(1,2) and vertical bar mu(x) - mu(0)vertical bar is suitably small, with mu(0) positive constant; an analogous result holds true for a bounded domain Omega subset of R-n (n>2) and weak solutions in W-1,W-n/2(Omega).
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相关论文
共 27 条
[1]  
CAMPANATO S., 1777, Ann. Mat. Pura Appl., V69, P321, DOI [10.1007/BF02414377, DOI 10.1007/BF02414377]
[2]   Improving the pressure accuracy in a projection scheme for incompressible fluids with variable viscosity [J].
Deteix, J. ;
Yakoubi, D. .
APPLIED MATHEMATICS LETTERS, 2018, 79 :111-117
[3]   The Stokes Paradox in Inhomogeneous Elastostatics [J].
Ferone, Adele ;
Russo, Remigio ;
Tartaglione, Alfonsina .
JOURNAL OF ELASTICITY, 2020, 142 (01) :35-52
[4]  
Galdi GP, 2011, SPRINGER MONOGR MATH, P1, DOI 10.1007/978-0-387-09620-9
[5]   A note on the evolution Navier-Stokes equations with a pressure-dependent viscosity [J].
Gazzola, F .
ZEITSCHRIFT FUR ANGEWANDTE MATHEMATIK UND PHYSIK, 1997, 48 (05) :760-773
[6]   STATIONARY SOLUTIONS TO THE NAVIER-STOKES EQUATIONS IN DIMENSION 4 [J].
GERHARDT, C .
MATHEMATISCHE ZEITSCHRIFT, 1979, 165 (02) :193-197
[7]  
GIAQUINTA M, 1982, J REINE ANGEW MATH, V330, P173
[8]  
GILBARG D., 1998, GRUNDLEHREN MATH WIS, V2nd
[9]  
Giusti E., 2004, DIRECT METHODS CALCU
[10]  
Happel J., 1973, Mechanics of Fluids and Transport Processes, V1, DOI DOI 10.1007/978-94-009-8352-6
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