Uniqueness for the two-dimensional Navier-Stokes equation with a measure as initial vorticity
TLDR
In this paper, it was shown that the Navier-stokes equation is well-posed for arbitrary data in a function space that is large enough to contain the initial data of some self-similar solutions.Citations
More filters
Journal ArticleDOI
New asymptotic profiles of nonstationary solutions of the Navier–Stokes system
TL;DR: In this paper, it was shown that solutions of the Navier-Stokes system with mild decaying data behave as potential fields as a potential field, where γd is the energy matrix of the flow.
Journal ArticleDOI
Propagation of chaos for the 2D viscous vortex model
TL;DR: In this paper, the authors consider a stochastic system of vortices and show that the empirical measure of the particle system converges in law to the unique (under suitable a priori estimates) solution of the 2D Navier-Stokes equation.
Journal ArticleDOI
Interaction of Vortices in Weakly Viscous Planar Flows
TL;DR: In this paper, the inviscid limit for the Navier-Stokes equation is considered in the case where the initial flow is a finite collection of point vortices.
Book ChapterDOI
The inviscid limit and boundary layers for navier-stokes flows
TL;DR: The validity of the vanishing viscosity limit, that is, whether solutions of the Navier-Stokes equations modeling viscous incompressible flows converges to solutions of Euler equations modeling inviscid incompressibly flows as viscoity approaches zero, is one of the most fundamental issues in mathematical fluid mechanics.
Journal ArticleDOI
Two-dimensional incompressible viscous flow around a small obstacle
TL;DR: In this paper, the authors studied the asymptotic behavior of incompressible, ideal, time-dependent two dimensional flow in the exterior of a single smooth obstacle when the size of the obstacle becomes very small.
References
More filters
Book
Geometric Theory of Semilinear Parabolic Equations
TL;DR: The neighborhood of an invariant manifold near an equilibrium point is a neighborhood of nonlinear parabolic equations in physical, biological and engineering problems as mentioned in this paper, where the neighborhood of a periodic solution is defined by the invariance of the manifold.
Book
Navier-Stokes Equations: Theory and Numerical Analysis
TL;DR: This paper presents thediscretization of the Navier-Stokes Equations: General Stability and Convergence Theorems, and describes the development of the Curl Operator and its application to the Steady-State Naviers' Equations.
Related Papers (5)
Global Stability of Vortex Solutions of the Two-Dimensional Navier-Stokes Equation
Thierry Gallay,C. Eugene Wayne +1 more
Invariant Manifolds and the Long-Time Asymptotics of the Navier-Stokes and Vorticity Equations on R2
Thierry Gallay,C. Eugene Wayne +1 more