Displaying similar documents to “Regularity criterion for a nonhomogeneous incompressible Ginzburg-Landau-Navier-Stokes system”

Self-improving bounds for the Navier-Stokes equations

Jean-Yves Chemin, Fabrice Planchon (2012)

Bulletin de la Société Mathématique de France

Similarity:

We consider regular solutions to the Navier-Stokes equation and provide an extension to the Escauriaza-Seregin-Sverak blow-up criterion in the negative regularity Besov scale, with regularity arbitrarly close to - 1 . Our results rely on turning a priori bounds for the solution in negative Besov spaces into bounds in the positive regularity scale.

Long-Time Asymptotics for the Navier-Stokes Equation in a Two-Dimensional Exterior Domain

Thierry Gallay (2012)

Journées Équations aux dérivées partielles

Similarity:

We study the long-time behavior of infinite-energy solutions to the incompressible Navier-Stokes equations in a two-dimensional exterior domain, with no-slip boundary conditions. The initial data we consider are finite-energy perturbations of a smooth vortex with small circulation at infinity, but are otherwise arbitrarily large. Using a logarithmic energy estimate and some interpolation arguments, we prove that the solution approaches a self-similar Oseen vortex as t → ∞ . This result was...

Serrin-type regularity criterion for the Navier-Stokes equations involving one velocity and one vorticity component

Zujin Zhang (2018)

Czechoslovak Mathematical Journal

Similarity:

We consider the Cauchy problem for the three-dimensional Navier-Stokes equations, and provide an optimal regularity criterion in terms of u 3 and ω 3 , which are the third components of the velocity and vorticity, respectively. This gives an affirmative answer to an open problem in the paper by P. Penel, M. Pokorný (2004).

On the Stokes and Navier-Stokes flows in a perturbed half-space

Takayuki Kubo, Yoshihiro Shibata (2005)

Banach Center Publications

Similarity:

We give the L p - L q estimate for the Stokes semigroup in a perturbed half-space and some global in time existence theorems for small solutions to the Navier-Stokes equation.

Regularity criterion for 3D Navier-Stokes equations in terms of the direction of the velocity

Alexis Vasseur (2009)

Applications of Mathematics

Similarity:

In this short note we give a link between the regularity of the solution u to the 3D Navier-Stokes equation and the behavior of the direction of the velocity u / | u | . It is shown that the control of Div ( u / | u | ) in a suitable L t p ( L x q ) norm is enough to ensure global regularity. The result is reminiscent of the criterion in terms of the direction of the vorticity, introduced first by Constantin and Fefferman. However, in this case the condition is not on the vorticity but on the velocity itself. The proof, based...

On the Ladyzhenskaya-Smagorinsky turbulence model of the Navier-Stokes equations in smooth domains. The regularity problem

Hugo Beirão da Veiga (2009)

Journal of the European Mathematical Society

Similarity:

We establish regularity results up to the boundary for solutions to generalized Stokes and Navier–Stokes systems of equations in the stationary and evolutive cases. Generalized here means the presence of a shear dependent viscosity. We treat the case p ≥ 2 . Actually, we are interested in proving regularity results in L q ( Ω ) spaces for all the second order derivatives of the velocity and all the first order derivatives of the pressure. The main aim of the present paper is to extend our previous...

Ill-posedness for the Navier-Stokes and Euler equations in Besov spaces

Yanghai Yu, Fang Liu (2024)

Applications of Mathematics

Similarity:

We construct a new initial data to prove the ill-posedness of both Navier-Stokes and Euler equations in weaker Besov spaces in the sense that the solution maps to these equations starting from u 0 are discontinuous at t = 0 .

Long-time behavior for 2D non-autonomous g-Navier-Stokes equations

Cung The Anh, Dao Trong Quyet (2012)

Annales Polonici Mathematici

Similarity:

We study the first initial boundary value problem for the 2D non-autonomous g-Navier-Stokes equations in an arbitrary (bounded or unbounded) domain satisfying the Poincaré inequality. The existence of a weak solution to the problem is proved by using the Galerkin method. We then show the existence of a unique minimal finite-dimensional pullback σ -attractor for the process associated to the problem with respect to a large class of non-autonomous forcing terms. Furthermore, when the force...

On the stability of compressible Navier-Stokes-Korteweg equations

Tong Tang, Hongjun Gao (2014)

Annales Polonici Mathematici

Similarity:

We consider the compressible Navier-Stokes-Korteweg (N-S-K) equations. Through a remarkable identity, we reveal a relationship between the quantum hydrodynamic system and capillary fluids. Using some interesting inequalities from quantum fluids theory, we prove the stability of weak solutions for the N-S-K equations in the periodic domain Ω = N , when N=2,3.

A global existence result for the compressible Navier-Stokes-Poisson equations in three and higher dimensions

Zhensheng Gao, Zhong Tan (2012)

Annales Polonici Mathematici

Similarity:

The paper is dedicated to the global well-posedness of the barotropic compressible Navier-Stokes-Poisson system in the whole space ℝ N with N ≥ 3. The global existence and uniqueness of the strong solution is shown in the framework of hybrid Besov spaces. The initial velocity has the same critical regularity index as for the incompressible homogeneous Navier-Stokes equations. The proof relies on a uniform estimate for a mixed hyperbolic/parabolic linear system with a convection term. ...

On an existence theorem for the Navier-Stokes equations with free slip boundary condition in exterior domain

Rieko Shimada, Norikazu Yamaguchi (2008)

Banach Center Publications

Similarity:

This paper deals with a nonstationary problem for the Navier-Stokes equations with a free slip boundary condition in an exterior domain. We obtain a global in time unique solvability theorem and temporal asymptotic behavior of the global strong solution when the initial velocity is sufficiently small in the sense of Lⁿ (n is dimension). The proof is based on the contraction mapping principle with the aid of L p - L q estimates for the Stokes semigroup associated with a linearized problem, which...

Existence, uniqueness and regularity of stationary solutions to inhomogeneous Navier-Stokes equations in ℝ n

Reinhard Farwig, Hermann Sohr (2009)

Czechoslovak Mathematical Journal

Similarity:

For a bounded domain Ω ⊂ ℝ n , n ≥ 3 , we use the notion of very weak solutions to obtain a new and large uniqueness class for solutions of the inhomogeneous Navier-Stokes system - Δ u + u · ∇ u + ∇ p = f , div u = k , u | ∂ Ω = g with u ∈ L q , q ≥ n , and very general data classes for f , k , g such that u may have no differentiability property. For smooth data we get a large class of unique and regular solutions extending well known classical solution classes, and generalizing regularity results. Moreover, our results are closely related to those of...

On the existence for the Dirichlet problem for the compressible linearized Navier-Stokes system in the L p -framework

Piotr Boguslaw Mucha, Wojciech Zajączkowski (2002)

Annales Polonici Mathematici

Similarity:

The existence of solutions to the Dirichlet problem for the compressible linearized Navier-Stokes system is proved in a class such that the velocity vector belongs to W r 2 , 1 with r > 3. The proof is done in two steps. First the existence for local problems with constant coefficients is proved by applying the Fourier transform. Next by applying the regularizer technique the existence in a bounded domain is shown.