English
Related papers

Related papers: Regularity Criterion for Solutions of Three-Dimens…

200 papers

The Navier-Stokes-Voigt model of viscoelastic incompressible fluid has been recently proposed as a regularization of the three-dimensional Navier-Stokes equations for the purpose of direct numerical simulations. Besides the kinematic…

Mathematical Physics · Physics 2009-10-09 Fabio Ramos , Edriss S. Titi

We investigate parameteric Navier-Stokes equations for a viscous, incompressible flow in bounded domains. The coefficients of the equations are perturbed by high-dimensional random parameters, this fits in particular for modelling flows in…

Numerical Analysis · Mathematics 2025-04-21 Alexey Chernov , Tung Le

In this work we investigate the question of preventing the three-dimensional, incompressible Navier-Stokes equations from developing singularities, by controlling one component of the velocity field only, in space-time scale invariant…

Analysis of PDEs · Mathematics 2018-07-27 Jean-Yves Chemin , Isabella Gallagher , Ping Zhang

We continue our work reported earlier (A. Muriel and M. Dresden, Physica D 101, 299, 1997) to calculate the time evolution of the one-particle distribution function. An improved operator formalism, heretofore unexplored, is used for uniform…

Mathematical Physics · Physics 2010-12-01 Amador Muriel

We have developed dynamic manifold solutions for the Navier-Stokes equations using an extension of differential geometry called the calculus for moving surfaces. Specifically, we have shown that the geometric solutions to the Navier-Stokes…

Analysis of PDEs · Mathematics 2024-05-27 David V. Svintradze

Higher moments of the vorticity field $\Omega_{m}(t)$ in the form of $L^{2m}$-norms ($1 \leq m < \infty$) are used to explore the regularity problem for solutions of the three-dimensional incompressible Navier-Stokes equations on the domain…

Chaotic Dynamics · Physics 2015-05-13 J. D. Gibbon

In this paper, we establish vanishing viscosity limit of the 2D Navier-Stokes equations in a horizontally periodic strip. On the vertical direction, the horizontal component of the velocity is subjected to two different types of boundary…

Analysis of PDEs · Mathematics 2024-04-30 Mingwen Fei , Xinghong Pan , Jianfeng Zhao

This paper extends the resolvent formalism for wall turbulence proposed by McKeon and Sharma(2010) to account for the effect of streamwise-constant riblets. Under the resolvent formulation, the Navier-Stokes equations are interpreted as a…

Fluid Dynamics · Physics 2021-01-15 Andrew Chavarin , Mitul Luhar

We study the nonlinear stability of the two-dimensional Navier-Stokes equations around the Couette shear flow in the channel domain $\mathbb{R}\times[-1,1]$ subject to Navier slip boundary conditions. We establish a quantitative stability…

Analysis of PDEs · Mathematics 2025-09-04 Tao Liang , Jiahong Wu , Xiaoping Zhai

We prove geometrically improved version of Prodi-Serrin type blow-up criterion. Let $v$ and $\omega$ be the velocity and the vorticity of solutions to the 3D Navier-Stokes equations and denote $\{f\}_+=\max\{f, 0\}$ , $Q_T=\Bbb R^3\times…

Analysis of PDEs · Mathematics 2016-08-31 Dongho Chae , Jihoon Lee

A class of sufficient conditions of local regularity for suitable weak solutions to the nonstationary three-dimensional Navier-Stokes equations are discussed. The corresponding results are formulated in terms of functionals which are…

Analysis of PDEs · Mathematics 2007-05-23 G Seregin

Numerical solvers of the incompressible Navier-Stokes equations have reproduced turbulence phenomena such as the law of the wall, the dependence of turbulence intensities on the Reynolds number, and experimentally observed properties of…

Fluid Dynamics · Physics 2015-06-05 Divakar Viswanath , Ian Tobasco

We study the nonhomogeneous boundary value problem for Navier-Stokes equations of steady motion of a viscous incompressible fluid in a three-dimensional bounded multiply connected domain. We prove that this problem has a solution in some…

Mathematical Physics · Physics 2012-04-12 Mikhail Korobkov , Konstantin Pileckas , Remigio Russo

The 3D spatially periodic Navier-Stokes equation is posed as a nonlinear matrix differential equation. When the flow is assumed to be a time series having unknown wavenumber coefficients, then the matrix in this periodic Navier-Stokes…

Analysis of PDEs · Mathematics 2008-08-28 David T. Purvance

In this paper we prove the existence and uniqueness of path-wise strong solution to stochastic viscous flow in unbounded channels with multiple outlets using local monotonicity arguments. We devise a construction for solvability using a…

Probability · Mathematics 2014-12-22 Utpal Manna , Manil T. Mohan , Sivaguru S. Sritharan

In this article, we study regularity criteria for the 3D micropolar fluid equations in terms of one partial derivative of the velocity. It is proved that if \begin{equation*}…

Analysis of PDEs · Mathematics 2020-06-02 Fan Wu , Maria Alessandra Ragusa

In this paper, we study the Navier-Stokes equations of compressible, barotropic flow posed in a bounded set in $\mathbb{R}^3$ with different boundary conditions. Specifically, we prove that the local-in-time smooth solution of the…

Analysis of PDEs · Mathematics 2020-11-24 Anthony Suen

In the note, a local regularity condition for axisymmetric solutions to the non-stationary 3D Navier-Stokes equations is proven. It reads that axially symmetric energy solutions to the Navier-Stokes equations have no Type I blowups.

Analysis of PDEs · Mathematics 2020-06-09 G. Seregin

We consider a finite volume scheme for the two-dimensional incompressible Navier-Stokes equations. We use a triangular mesh. The unknowns for the velocity and pressure are respectively piecewise constant and affine. We use a projection…

Numerical Analysis · Mathematics 2007-05-23 Sebastien Zimmermann

We present new interior regularity criteria for suitable weak solutions of the 3-D Navier-Stokes equations: a suitable weak solution is regular near an interior point $z$ if either the scaled $L^{p,q}_{x,t}$-norm of the velocity with…

Analysis of PDEs · Mathematics 2009-11-11 Stephen Gustafson , Kyungkeun Kang , Tai-Peng Tsai