On the Euler plus Prandtl Expansion for the Navier-Stokes Equations

被引：0

作者：

Kukavica, Igor ^{[1
]}

Nguyen, Trinh T. ^{[1
]}

Vicol, Vlad ^{[2
]}

Wang, Fei ^{[3
]}

机构：

[1] Univ Southern Calif, Dept Math, Los Angeles, CA 90089 USA

[2] NYU, Courant Inst Math Sci, New York, NY 10012 USA

[3] Shanghai Jiao Tong Univ, Sch Math Sci, CMA Shanghai, Shanghai, Peoples R China

来源：

JOURNAL OF MATHEMATICAL FLUID MECHANICS | 2022年 / 24卷 / 02期

基金：

美国国家科学基金会;

关键词：

Inviscid limit; Navier-Stokes equations; Euler equations; Prandtl expansion; Analyticity; ZERO-VISCOSITY LIMIT; VANISHING VISCOSITY; INVISCID LIMIT; BOUNDARY-LAYER; ANALYTIC SOLUTIONS; WELL-POSEDNESS; ILL-POSEDNESS; VORTICITY EQUATIONS; HALF-SPACE; EXISTENCE;

D O I：

10.1007/s00021-021-00645-4

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We establish the validity of the Euler+Prandtl approximation for solutions of the Navier-Stokes equations in the half plane with the Dirichlet boundary conditions, in the vanishing viscosity limit, for initial data which are analytic only near the boundary, and Sobolev smooth away from the boundary. Our proof does not require higher order correctors, and works directly by estimating an L-1-type norm for the vorticity of the error term in the expansion Navier-Stokes-(Euler+Prandtl). An important ingredient in the proof is the propagation of local analyticity for the Euler equation, a result of independent interest

引用

页数：46

共 62 条

[41] THE DOMAIN OF ANALYTICITY OF SOLUTIONS TO THE THREE-DIMENSIONAL EULER EQUATIONS IN A HALF SPACE [J].

Kukavica, Igor ;

Vicol, Vlad C. .

DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS, 2011, 29 (01) :285-303

[42]

Li W.J., 2016, INT JOINT C ARTIFICI, P1711

[43] Ill-posedness of the Prandtl equations in Sobolev spaces around a shear flow with general decay [J].

Liu, Cheng-Jie ;

Yang, Tong .

JOURNAL DE MATHEMATIQUES PURES ET APPLIQUEES, 2017, 108 (02) :150-162

[44] Well-posedness of the boundary layer equations [J].

Lombardo, MC ;

Cannone, M ;

Sammartino, M .

SIAM JOURNAL ON MATHEMATICAL ANALYSIS, 2003, 35 (04) :987-1004

[45] Zero viscosity limit of the Oseen equations in a channel [J].

Lombardo, MC ;

Sammartino, M .

SIAM JOURNAL ON MATHEMATICAL ANALYSIS, 2001, 33 (02) :390-410

[46] Vanishing viscosity limit for incompressible flow inside a rotating circle [J].

Lopes Filho, M. C. ;

Mazzucato, A. L. ;

Lopes, H. J. Nussenzveig .

PHYSICA D-NONLINEAR PHENOMENA, 2008, 237 (10-12) :1324-1333

[47] Vanishing viscosity limits and boundary layers for circularly symmetric 2D flows [J].

Lopes Filho, M. C. ;

Mazzucato, A. L. ;

Nussenzveig Lopes, H. J. ;

Taylor, Michael .

BULLETIN OF THE BRAZILIAN MATHEMATICAL SOCIETY, 2008, 39 (04) :471-513

[48]

Maekawa Y., 2016, Handbook of Mathematical Analysis in Mechanics of Viscous Fluids, P1

[49] On the Inviscid Limit Problem of the Vorticity Equations for Viscous Incompressible Flows in the Half-Plane [J].

Maekawa, Yasunori .

COMMUNICATIONS ON PURE AND APPLIED MATHEMATICS, 2014, 67 (07) :1045-1128

[50]

Maekawa Y, 2013, ADV DIFFERENTIAL EQU, V18, P101

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