# Lagrangian solutions to the 2D euler system with L^1 vorticity and infinite energy

@article{Bohun2015LagrangianST, title={Lagrangian solutions to the 2D euler system with L^1 vorticity and infinite energy}, author={Anna Bohun and François Bouchut and Gianluca Crippa}, journal={arXiv: Analysis of PDEs}, year={2015} }

## 14 Citations

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

- Mathematics, Environmental Science
- 2021

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…

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

- Mathematics, PhysicsJ. 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.

Vorticity convergence from Boltzmann to 2D incompressible Euler equations below Yudovich class

- Mathematics, Physics
- 2022

We obtain a microscopic description of the singularity through the so-called kinetic vorticity and understand its behavior in the vicinity of the macroscopic singularity. As a consequence of our new…

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…

Renormalization and energy conservation for axisymmetric fluid flows

- Physics, MathematicsMathematische Annalen
- 2020

We study vanishing viscosity solutions to the axisymmetric Euler equations without swirl with (relative) vorticity in $$L^p$$ L p with $$p>1$$ p > 1 . We show that these solutions satisfy the…

Lagrangian solutions to the Vlasov-Poisson system with a point charge

- Mathematics
- 2017

We consider the Cauchy problem for the repulsive Vlasov-Poisson system in the three dimensional space, where the initial datum is the sum of a diffuse density, assumed to be bounded and integrable,…

Existence of weak solutions to the two-dimensional incompressible Euler equations in the presence of sources and sinks

- Mathematics
- 2021

A classical model for sources and sinks in a two-dimensional perfect incompressible fluid occupying a bounded domain dates back to Yudovich’s paper [44] in 1966. In this model, on the one hand, the…

A P ] 2 7 A ug 2 02 0 STRONG CONVERGENCE OF THE VORTICITY FOR THE 2 D EULER EQUATIONS IN THE INVISCID LIMIT

- Mathematics
- 2020

In this paper we prove that, if (u, ω) is a renormalized/Lagrangian solution of the 2D Euler equations with ω in L uniformly in time obtained as inviscid limit of solutions (u , ω) of the 2D…

Eulerian and Lagrangian Solutions to the Continuity and Euler Equations with L1 Vorticity

- MathematicsSIAM J. Math. Anal.
- 2017

This paper addresses a question that arose in \cite{FilhoMazzucatoNussenzveig06}, namely whether 2D Euler solutions obtained via vanishing viscosity are renormalized when the initial data has low integrability.

## References

SHOWING 1-10 OF 27 REFERENCES

The weak vorticity formulation of the 2-D Euler equations and concentration-cancellation

- Mathematics
- 1995

The weak limit of a sequence of approximate solutions of the 2-D Euler equations will be a solution if the approximate vorticities concentrate only along a curve x(t) that is Holder continuous with…

Vorticity and incompressible flow

- Mathematics
- 2001

Preface 1. An introduction to vortex dynamics for incompressible fluid flows 2. The vorticity-stream formulation of the Euler and the Navier-Stokes equations 3. Energy methods for the Euler and the…

Oscillations and concentrations in weak solutions of the incompressible fluid equations

- Mathematics
- 1987

The authors introduce a new concept of measure-valued solution for the 3-D incompressible Euler equations in order to incorporate the complex phenomena present in limits of approximate solutions of…

Uniqueness Theorem for the Basic Nonstationary Problem in the Dynamics of an Ideal Incompressible Fluid

- Mathematics
- 1995

A bstract . The initial boundary value problem is considered for the Euler equations for an incompressible fluid in a bounded domain D ⊂ Rn. It is known [Y1] that uniqueness holds for those flows…

OnL1-vorticity for 2-D incompressible flow

- Mathematics
- 1993

We prove the existence of a classical weak solution for the 2-D incompressible Euler equations with initial vorticity ω0=ω0′ + ω0″, where ω0′ is inL1(R2)⌢H−1(R2), compactly supported, and ω0″ is a…

Lagrangian flows for vector fields with gradient given by a singular integral

- Mathematics
- 2013

We prove quantitative estimates on flows of ordinary differential equations with vector field with gradient given by a singular integral of an L1 function. Such estimates allow to prove existence,…

Mathematical Theory of Incompressible Nonviscous Fluids

- Mathematics
- 1993

This book deals with fluid dynamics of incompressible non-viscous fluids. The main goal is to present an argument of large interest for physics, and applications in a rigorous logical and…

Reduced Hausdorff dimension and concentration-cancellation for two-dimensional incompressible flow

- Mathematics
- 1988

where v = t(v1 , v2) is the fluid velocity, p is the scalar pressure, Dv/Dt av/at+(v.V)v, and vo is an initial incompressible velocity field, i.e. div vo = 0. In this paper, we study the detailed…