Algebraic decay rates for 3D Navier-Stokes and Navier-Stokes-Coriolis equations in H•1/2

被引：0

作者：

Ikeda, Masahiro ^{[1
,2
]}

Kosloff, Leonardo ^{[3
]}

Niche, Cesar J. ^{[4
]}

Planas, Gabriela ^{[5
]}

机构：

[1] Keio Univ, Fac Sci & Technol, Dept Math, 3-14-1 Hiyoshi,Kohoku Ku, Yokohama 2238522, Japan

[2] RIKEN, Ctr Adv Intelligence Project, Wako, Japan

[3] Univ Estadual Campinas, Inst Matemat Estat & Computacao Cient, Dept Matemat, Rua Sergio Buarque Holanda 651, BR-13083859 Campinas, SP, Brazil

[4] Univ Fed Rio De Janeiro, Inst Matemat, Dept Matemat Aplicada, BR-21941909 Rio De Janeiro, RJ, Brazil

[5] Univ Estadual Campinas, Inst Matemat Estat & Computacao Cient, Dept Matemat, Rua Sergio Buarque Holanda 651, BR-13083859 Campinas, SP, Brazil

来源：

JOURNAL OF EVOLUTION EQUATIONS | 2024年 / 24卷 / 03期

基金：

巴西圣保罗研究基金会;

关键词：

Decay rates; Navier-Stokes; Navier-Stokes-Coriolis; Critical spaces; WEAK SOLUTIONS; ILL-POSEDNESS;

D O I：

10.1007/s00028-024-00991-6

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

An algebraic upper bound for the decay rate of solutions to the Navier-Stokes and Navier-Stokes-Coriolis equations in the critical space H(center dot)1/2 is derived using the Fourier splitting method. Estimates are framed in terms of the decay character of initial data, leading to solutions with algebraic decay and showing in detail the roles played by the linear and nonlinear parts. The proof is carried on purely in the critical space, as no L-2(R-3) estimates are available for the solution. This is the first instance in which such a method is used for obtaining decay bounds in a critical space for a nonlinear equation.

引用

页数：25

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