Global regularity of density patch for the 3D inhomogeneous Navier-Stokes equations

被引：1

作者：

Chen, Qionglei ^{[1
]}

Li, Yatao ^{[2
]}

机构：

[1] Inst Appl Phys & Computat Math, Beijing 100088, Peoples R China

[2] China Acad Engn Phys, Grad Sch, Beijing 100088, Peoples R China

来源：

ZEITSCHRIFT FUR ANGEWANDTE MATHEMATIK UND PHYSIK | 2020年 / 71卷 / 02期

基金：

美国国家科学基金会;

关键词：

Inhomogeneous Navier-Stokes equations; Density patch; Singular kernels; FLUIDS; FLOW;

D O I：

10.1007/s00033-020-1263-3

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

This paper is concerning with the regularity propagation of density patches for the 3D inhomogeneous incompressible Navier-Stokes equations. By careful time-weighted energy estimates, Stokes estimates and the singular integral operators, we prove that the 3D density patches preserve the Ck,gamma(k=1,2) regularity for the initial interface given by rho 0(x)=eta 11 omega 0+eta 21 omega 0c. In particular, we do not need the smallness assumption on |eta 1-eta 2|.

引用

页数：18

共 25 条

[1]

Abidi H, 2007, REV MAT IBEROAM, V23, P537

[2]

Antontsev S.N., 1990, Boundary Value Problems in Mechanics of Nonhomogeneous Fluids, VVolume 22

[3] GLOBAL REGULARITY FOR VORTEX PATCHES [J].

BERTOZZI, AL ;

CONSTANTIN, P .

COMMUNICATIONS IN MATHEMATICAL PHYSICS, 1993, 152 (01) :19-28

[4] MOVEMENT OF PARTICLES OF A 2-DIMENSIONAL INCOMPRESSIBLE PERFECT FLUID [J].

CHEMIN, JY .

INVENTIONES MATHEMATICAE, 1991, 103 (03) :599-629

[5]

CHEMIN JY, 1993, ANN SCI ECOLE NORM S, V26, P517

[6] Fujita-Kato theorem for the 3-D inhomogeneous Navier-Stokes equations [J].

Chen, Dongxiang ;

Mang, Zhifei ;

Zhao, Weiren .

JOURNAL OF DIFFERENTIAL EQUATIONS, 2016, 261 (01) :738-761

[7] Density-dependent incompressible viscous fluids in critical spaces [J].

Danchin, R .

PROCEEDINGS OF THE ROYAL SOCIETY OF EDINBURGH SECTION A-MATHEMATICS, 2003, 133 :1311-1334

[8]

Danchin R, 2017, J ECOLE POLYTECH-MAT, V4, P781, DOI 10.5802/jep.56

[9] A Lagrangian Approach for the Incompressible Navier-Stokes Equations with Variable Density [J].

Danchin, Raphael ;

Mucha, Piotr Boguslaw .

COMMUNICATIONS ON PURE AND APPLIED MATHEMATICS, 2012, 65 (10) :1458-1480

[10] ORDINARY DIFFERENTIAL-EQUATIONS, TRANSPORT-THEORY AND SOBOLEV SPACES [J].

DIPERNA, RJ ;

LIONS, PL .

INVENTIONES MATHEMATICAE, 1989, 98 (03) :511-547

← 1 2 3 →