Markov solutions for the 3D stochastic Navier-Stokes equations with state dependent noise

被引：36

作者：

Debussche, A

Odasso, C

机构：

[1] IRMAR, F-35170 Bruz, France

[2] Ecole Normale Super, F-35170 Bruz, France

来源：

JOURNAL OF EVOLUTION EQUATIONS | 2006年 / 6卷 / 02期

关键词：

stochastic Navier-Stokes equations; Markov solutions; invariant measure; ergodicity;

D O I：

10.1007/s00028-006-0254-y

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We construct a Markov family of solutions for the 3D Navier-Stokes equations perturbed by a non degenerate noise. We improve the result of [3] in two directions. We see that in fact not only a transition semigroup but a Markov family of solutions can be constructed. Moreover, we consider a state dependant noise. Another feature of this work is that we greatly simplify the proofs of [3].

引用

页码：305 / 324

页数：20

共 50 条

[31] STOCHASTIC NAVIER-STOKES EQUATIONS WITH MULTIPLICATIVE NOISE
BRZEZNIAK, Z
CAPINSKI, M
FLANDOLI, F
[J]. STOCHASTIC ANALYSIS AND APPLICATIONS, 1992, 10 (05) : 523 - 532
[32] The 3D Navier-Stokes equations seen as a perturbation of the 2D Navier-Stokes equations
Iftimie, D
[J]. COMPTES RENDUS DE L ACADEMIE DES SCIENCES SERIE I-MATHEMATIQUE, 1997, 324 (03): : 271 - 274
[33] The 3D Navier-Stokes equations seen as a perturbation of the 2D Navier-Stokes equations
Iftimie, D
[J]. BULLETIN DE LA SOCIETE MATHEMATIQUE DE FRANCE, 1999, 127 (04): : 473 - 517
[34] Spatially homogeneous solutions of 3D stochastic Navier-Stokes equations and local energy inequality
Basson, Arnaud
[J]. STOCHASTIC PROCESSES AND THEIR APPLICATIONS, 2008, 118 (03) : 417 - 451
[35] MARTINGALE SOLUTIONS FOR STOCHASTIC NAVIER-STOKES EQUATIONS DRIVEN BY LEVY NOISE
Sakthivel, Kumarasamy
Sritharan, Sivaguru S.
[J]. EVOLUTION EQUATIONS AND CONTROL THEORY, 2012, 1 (02): : 355 - 392
[36] LP-solutions for stochastic Navier-Stokes equations with jump noise
Zhu, Jiahui
Brzeniak, Zdzislaw
Liu, Wei
[J]. STATISTICS & PROBABILITY LETTERS, 2019, 155
[37] STATISTICAL SOLUTIONS OF STOCHASTIC NAVIER-STOKES EQUATIONS
CAPINSKI, M
CUTLAND, NJ
[J]. INDIANA UNIVERSITY MATHEMATICS JOURNAL, 1994, 43 (03) : 927 - 940
[38] Regularity of weak solutions to 3D incompressible Navier-Stokes equations
Han, Pigong
[J]. JOURNAL OF EVOLUTION EQUATIONS, 2010, 10 (01) : 195 - 204
[39] Dynamically stretched vortices as solutions of the 3D Navier-Stokes equations
Gibbon, J.D.
Fokas, A.S.
Doering, C.R.
[J]. Physica D: Nonlinear Phenomena, 1999, 132 (04): : 497 - 510
[40] The 3D Navier-Stokes Equations: Invariants, Local and Global Solutions
Semenov, Vladimir, I
[J]. AXIOMS, 2019, 8 (02)

← 1 2 3 4 5 →