Length of vorticity nodal sets for solutions of the 2D Navier-Stokes equations

被引：9

作者：

Kukavica, I ^{[1
]}

机构：

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

来源：

COMMUNICATIONS IN PARTIAL DIFFERENTIAL EQUATIONS | 2003年 / 28卷 / 3-4期

关键词：

D O I：

10.1081/PDE-120020496

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We provide an upper bound on the size of the nodal set {x is an element of Omega : omega(x, t) = 0} of the vorticity omega for solutions of the 2D periodic Navier-Stokes equation. The upper bound depends polynomially on the initial condition, viscosity, the size of 2, and 1/t. The result is based on a new bound on the order of vanishing for solutions of partial derivativeu/partial derivativet - Deltau = w (.) delu + vu.

引用

页码：771 / 793

页数：23

共 50 条

[31] RESOLUTION OF THE 2D NAVIER-STOKES EQUATIONS IN VELOCITY VORTICITY FORM BY MEANS OF AN INFLUENCE MATRIX TECHNIQUE
DAUBE, O
JOURNAL OF COMPUTATIONAL PHYSICS, 1992, 103 (02) : 402 - 414
[32] Uniform approximation of 2D Navier-Stokes equations with vorticity creation by stochastic interacting particle systems
Grotto, Francesco
Luongo, Eliseo
Maurelli, Mario
NONLINEARITY, 2023, 36 (12) : 7149 - 7190
[33] An immersed interface method for the 2D vorticity-velocity Navier-Stokes equations with multiple bodies
Gabbard, James
Gillis, Thomas
Chatelain, Philippe
van Rees, Wim M.
JOURNAL OF COMPUTATIONAL PHYSICS, 2022, 464
[34] A BOUNDARY CONTROL PROBLEM FOR VORTICITY MINIMIZATION IN TIME-DEPENDENT 2D NAVIER-STOKES EQUATIONS
Kim, Hongchul
KOREAN JOURNAL OF MATHEMATICS, 2015, 23 (02): : 293 - 312
[35] TIME-SPACE L2-BOUNDEDNESS FOR THE 2D NAVIER-STOKES EQUATIONS AND HYPERBOLIC NAVIER-STOKES EQUATIONS
Kobayashi, Takayuki
Misawa, Masashi
Nakamura, Kenji
TSUKUBA JOURNAL OF MATHEMATICS, 2019, 43 (02) : 223 - 239
[36] A PRIORI BOUNDS FOR THE VORTICITY OF AXIALLY SYMMETRIC SOLUTIONS TO THE NAVIER-STOKES EQUATIONS
Loftus, Jennifer Burke
Zhang, Qi S.
ADVANCES IN DIFFERENTIAL EQUATIONS, 2010, 15 (5-6) : 531 - 560
[37] VORTICITY AT INFINITY FOR SOLUTIONS OF STATIONARY NAVIER-STOKES EQUATIONS IN EXTERIOR DOMAINS
CLARK, DC
INDIANA UNIVERSITY MATHEMATICS JOURNAL, 1971, 20 (07) : 633 - &
[38] Global solutions of stochastic 2D Navier-Stokes equations with Lévy noise
Zhao Dong
YinChao Xie
Science in China Series A: Mathematics, 2009, 52 : 1497 - 1524
[39] Moments for strong solutions of the 2D stochastic Navier-Stokes equations in a bounded domain
Kukavica, Igor
Vicol, Vlad
ASYMPTOTIC ANALYSIS, 2014, 90 (3-4) : 189 - 206
[40] Global solutions of stochastic 2D Navier-Stokes equations with Lévy noise
DONG Zhao1 & XIE YinChao2 1 Institute of Applied Mathematics
Science China Mathematics, 2009, (07) : 1497 - 1524

← 1 2 3 4 5 →