The Lp-Lq decay estimate for the multidimensional compressible flow with free surface in the exterior domain

被引：2

作者：

Shibata, Yoshihiro ^{[1
,2
]}

Zhang, Xin ^{[3
]}

机构：

[1] Waseda Univ, Dept Math, Shinjuku Ku, Ohkubo 3-4-1, Tokyo 1698555, Japan

[2] Univ Pittsburgh, Dept Mech Engn & Mat Sci, Pittsburgh, PA USA

[3] Tongji Univ, Sch Math Sci, 1239 Siping Rd, Shanghai 200092, Peoples R China

来源：

JOURNAL OF DIFFERENTIAL EQUATIONS | 2022年 / 325卷

关键词：

Lame operator; Free boundary condition; Resolvent problem; Decay estimate; NAVIER-STOKES EQUATIONS; GLOBAL EXISTENCE; CRITICAL SPACES; SEMIGROUP; BEHAVIOR;

D O I：

10.1016/j.jde.2022.04.012

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

The aim of this paper is to develop the general Lp theory for the barotropic compressible Navier-Stokes equations with the free boundary condition in the exterior domain in RN (N >= 3). By the spectral analysis, we obtain the classical Lp-Lq decay estimate for the linearized model problem (with variable coefficients) in view of the partial Lagrangian transformation. (c) 2022 Elsevier Inc. All rights reserved.

引用

页码：150 / 205

页数：56

共 50 条

[11] Lp-Lq decay estimates of solutions to Cauchy problems of thermoviscoelastic systems
Yang Lin
Huang Li-hong
Kuang Feng-lian
APPLIED MATHEMATICS-A JOURNAL OF CHINESE UNIVERSITIES SERIES B, 2009, 24 (04) : 473 - 482
[12] Lp-Lq decay estimates for wave equations with time-dependent coefficients
Reissig, M
JOURNAL OF NONLINEAR MATHEMATICAL PHYSICS, 2004, 11 (04) : 534 - 548
[13] On the maximal Lp-Lq regularity for a compressible fluid model of Korteweg type on general domains
Saito, Hirokazu
JOURNAL OF DIFFERENTIAL EQUATIONS, 2020, 268 (06) : 2802 - 2851
[14] Pointwise estimates for oscillatory integrals and related Lp-Lq estimates II:: Multidimensional case
Cui, Shangbin
JOURNAL OF FOURIER ANALYSIS AND APPLICATIONS, 2006, 12 (06) : 605 - 627
[15] On the Lp-Lq maximal regularity for the linear thermoelastic plate equation in a bounded domain
Naito, Yuka
MATHEMATICAL METHODS IN THE APPLIED SCIENCES, 2009, 32 (13) : 1609 - 1637
[16] LP-Lq decay estimates for dissipative linear hyperbolic systems in 1D
Mascia, Corrado
Thinh Tien Nguyen
JOURNAL OF DIFFERENTIAL EQUATIONS, 2017, 263 (10) : 6189 - 6230
[17] Optimal Lp-Lq convergence rates for the compressible Navier-Stokes equations with potential force
Duan, Renjun
Liu, Hongxia
Ukai, Seiji
Yang, Tong
JOURNAL OF DIFFERENTIAL EQUATIONS, 2007, 238 (01) : 220 - 233
[18] Global solvability of the Navier-Stokes equations with a free surface in the maximal Lp-Lq regularity class
Saito, Hirokazu
JOURNAL OF DIFFERENTIAL EQUATIONS, 2018, 264 (03) : 1475 - 1520
[19] Lp-Lq Decay Estimates for Dissipative Linear Hyperbolic Systems in 1D
Mascia, Corrado
Thinh Tien Nguyen
THEORY, NUMERICS AND APPLICATIONS OF HYPERBOLIC PROBLEMS II, 2018, 237 : 305 - 319
[20] The Lp-Lq estimates of solutions to one-dimensional damped wave equations and their application to the compressible flow through porous media
Marcati, P
Nishihara, K
JOURNAL OF DIFFERENTIAL EQUATIONS, 2003, 191 (02) : 445 - 469

← 1 2 3 4 5 →