Strong Convergence of the Vorticity for the 2D Euler Equations in the Inviscid Limit

  title={Strong Convergence of the Vorticity for the 2D Euler Equations in the Inviscid Limit},
  author={Gennaro Ciampa and Gianluca Crippa and Stefano Spirito},
  journal={Archive for Rational Mechanics and Analysis},
<jats:p>In this paper we prove the uniform-in-time <jats:inline-formula><jats:alternatives><jats:tex-math>$$L^p$$</jats:tex-math><mml:math xmlns:mml=""> <mml:msup> <mml:mi>L</mml:mi> <mml:mi>p</mml:mi> </mml:msup> </mml:math></jats:alternatives></jats:inline-formula> convergence in the inviscid limit of a family <jats:inline-formula><jats:alternatives><jats:tex-math… 

Energy conservation for 2D Euler with vorticity in $L(\log L)^\alpha$

In these notes we discuss the conservation of the energy for weak solutions of the twodimensional incompressible Euler equations. Weak solutions with vorticity in L∞t L p x with p ≥ 3/2 are always

A few remarks on the transport-Stokes system

We consider the so-called transport-Stokes system which describes sedimentation of inertialess sus-pensions in a viscous flow and couples a transport equation and the steady Stokes equations in the

A KAM approach to the inviscid limit for the 2D Navier-Stokes equations

. In this paper we investigate the inviscid limit ν → 0 for time-quasi-periodic solutions of the incompressible Navier-Stokes equations on the two-dimensional torus T 2 , with a small

On maximum enstrophy dissipation in 2D Navier–Stokes flows in the limit of vanishing viscosity

Statistical solutions of the incompressible Euler equations

Analysis of statistical solutions of the incompressible Euler equations in two dimensions with vorticity in L p, 1 ≤ p ≤ ∞ , and in the class of vortex-sheets with a distinguished sign shows uniqueness of trajectory statistical solutions in the Yudovich class.

Propagation of singularities by Osgood vector fields and for 2D inviscid incompressible fluids

We show that certain singular structures (H¨olderian cusps and mild divergences) are transported by the flow of homeomorphisms generated by an Osgood velocity field. The structure of these

Energy balance for forced two-dimensional incompressible ideal fluid flow

Cheskidov et al. (2016 Commun. Math. Phys. 348, 129–143. (doi:10.1007/s00220-016-2730-8)) proved that physically realizable weak solutions of the incompressible two-dimensional Euler equations on a

Vanishing viscosity limits for the free boundary problem of compressible viscoelastic fluids with surface tension

We consider the free boundary problem of compressible isentropic neo-Hookean viscoelastic fluid equations with surface tension. Under the physical kinetic and dynamic conditions proposed on the free

Energy conservation in the limit of filtered solutions for the 2D Euler equations

We consider energy conservation in a two-dimensional incompressible and inviscid flow through weak solutions of the filtered-Euler equations, which describe a regularized Euler flow based on a

On the advection-diffusion equation with rough coefficients: weak solutions and vanishing viscosity



Inviscid Limit of Vorticity Distributions in the Yudovich Class

We prove that given initial data ω0∈L∞T2 , forcing g∈L∞0,T;L∞T2, and any T > 0, the solutions uν of Navier‐Stokes converge strongly in L∞0,T;W1,pT2 for any p ∈ [1, ∞) to the unique Yudovich weak

On the vanishing viscosity limit for 2D incompressible flows with unbounded vorticity

We show strong convergence of the vorticities in the vanishing viscosity limit for the incompressible Navier–Stokes equations on the two-dimensional torus, assuming only that the initial vorticity of

Dissipative Euler Flows for Vortex Sheet Initial Data without Distinguished Sign

We construct infinitely many admissible weak solutions to the 2D incompressible Euler equations for vortex sheet initial data. Our initial datum has vorticity concentrated on a simple closed curve in

A posteriori error estimates for self-similar solutions to the Euler equations

  • A. BressanWen Shen
  • Mathematics, Computer Science
    Discrete & Continuous Dynamical Systems - A
  • 2021
A system of equations corresponding to a self-similar solution, restricted to a bounded domain with smooth boundary, is considered, and a posteriori error bounds are established on the distance between the numerical approximation and the exact solution having the same boundary data.

A Note on the Vanishing Viscosity Limit in the Yudovich Class

Abstract We consider the inviscid limit for the two-dimensional Navier–Stokes equations in the class of integrable and bounded vorticity fields. It is expected that the difference between the

Weak Solutions Obtained by the Vortex Method for the 2D Euler Equations are Lagrangian and Conserve the Energy

It is proved that solutions obtained via the vortex method are Lagrangian, and that they are conservative if p>1, and if all weak solutions are conservative.

Energy Conservation in Two-dimensional Incompressible Ideal Fluids

This note addresses the issue of energy conservation for the 2D Euler system with an Lp-control on vorticity. We provide a direct argument, based on a mollification in physical space, to show that

Solutions C∞ en temps, n-log lipchitz bornées en espace et équation d'Euler

Sur tout [0, T], on resout l'equation d'Euler incompressible 2D en cadre L∞ sous-lipschitz [u, rot(u) bornes sans hypothese d'integrabilite] et on montre que la derivee n-ieme en t des solutins a C