An almost sure energy inequality for Markov solutions to the 3D Navier-Stokes equations [PDF]
arXiv, 2009 We prove existence of weak martingale solutions satisfying an almost sure version of the energy inequality and which constitute a (almost sure) Markov process.
Romito, Marco
arxiv +3 more sources
Large-time behavior of the weak solution to 3D Navier-Stokes equations [PDF]
, 2012 The weak solution to the Navier-Stokes equations in a bounded domain $D \subset \mathbb{R}^3$ with a smooth boundary is proved to be unique provided that it satisfies an additional requirement. This solution exists for all $t \geq 0$. In a bounded domain
A.G. Ramm +7 more
core +4 more sources
Existence and uniqueness of global solutions for the modified anisotropic 3D Navier-Stokes equations [PDF]
, 2016 We study a modified three-dimensional incompressible anisotropic Navier-Stokes equations. The modification consists in the addition of a power term to the nonlinear convective one.
Bessaih, Hakima +2 more
core +2 more sources
Conditions implying regularity of the three dimensional Navier-Stokes equation [PDF]
, 2004 We obtain logarithmic improvements for conditions for regularity of the Navier-Stokes equation, similar to those of Prodi-Serrin or Beale-Kato-Majda. Some of the proofs make use of a stochastic approach involving Feynman-Kac like inequalities. As part of
Jiang, Lingyu, Wang, Yidong
core +5 more sources
"Missing" boundary conditions? Discretize first, substitute next, and combine later [PDF]
, 1990 A simple approach exists to prevent the need for constructing boundary conditions in situations where they are not explicitly supplied by the original analytical formulation of the problem.
Veldman, Arthur E.P.,
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A Serrin-type regularity criterion for the Navier-Stokes equations via one velocity component [PDF]
Commu. Pure Appl. Anal., 12 (2013), 117--124, 2011 We study the Cauchy problem for the 3D Navier-Stokes equations, and prove some scalaring-invariant regularity criteria involving only one velocity component.
arxiv +1 more source
Ergodicity of Stochastically Forced Large Scale Geophysical Flows
, 2001 We investigate the ergodicity of 2D large scale quasigeostrophic flows under random wind forcing. We show that the quasigeostrophic flows are ergodic under suitable conditions on the random forcing and on the fluid domain, and under no restrictions on ...
Duan, Jinqiao, Goldys, Beniamin
core +2 more sources
Regularity Criterion to the axially symmetric Navier-Stokes Equations
, 2015 Smooth solutions to the axially symmetric Navier-Stokes equations obey the following maximum principle:$\|ru_\theta(r,z,t)\|_{L^\infty}\leq\|ru_\theta(r,z,0)\|_{L^\infty}.$ We first prove the global regularity of solutions if $\|ru_\theta(r,z,0)\|_{L ...
Wei, Dongyi
core +1 more source
Shear-flow transition: the basin boundary
, 2009 The structure of the basin of attraction of a stable equilibrium point is investigated for a dynamical system (W97) often used to model transition to turbulence in shear flows.
Eckhardt B +4 more
core +1 more source
Strong solution of 3D-NSE with exponential damping [PDF]
arXiv, 2021 In this paper we prove the existence and uniqueness of strong solution of the incompressible Navier-Stokes equations with damping $\alpha (e^{\beta|u|^2}-1)u$.
arxiv