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

@article{Ciampa2020StrongCO,
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},
year={2020}
}
• Published 27 August 2020
• Mathematics
• 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="http://www.w3.org/1998/Math/MathML"> <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…
15 Citations

### 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

• Mathematics
• 2022
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

• Mathematics
• 2022
. 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

### Statistical solutions of the incompressible Euler equations

• Mathematics, Computer Science
• 2022
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

• Mathematics
• 2022
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

• Physics
Philosophical Transactions of the Royal Society A
• 2022
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

• Mathematics
• 2022
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

## References

SHOWING 1-10 OF 44 REFERENCES

### Inviscid Limit of Vorticity Distributions in the Yudovich Class

• Mathematics
Communications on Pure and Applied Mathematics
• 2020
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

• Mathematics
• 2020
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

• Mathematics, Physics
Communications on Pure and Applied Mathematics
• 2022
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

• 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

• Mathematics, Physics
J. Nonlinear Sci.
• 2020
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

• Mathematics
• 2016
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