Optimal regularity for the 2D Euler equations in the Yudovich class

Smoothness and regularity of solutions to PDEs (35B65) PDEs in connection with fluid mechanics (35Q35) Vortex flows for incompressible inviscid fluids (76B47) Existence, uniqueness, and regularity theory for incompressible inviscid fluids (76B03)

Cites Work

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Small scale creation for solutions of the incompressible two-dimensional Euler equation
Transport equation and Cauchy problem for BV vector fields
Differentiability properties of the flow of 2d autonomous vector fields
Ordinary differential equations, transport theory and Sobolev spaces
Uniqueness of signed measures solving the continuity equation for Osgood vector fields
Remarks on the breakdown of smooth solutions for the 3-D Euler equations
On nonstationary flows of viscous and ideal fluids in \(L^ p_ s({\mathbb{R}}^ 2)\)
Hydrodynamics in Besov spaces
Mathematical theory of incompressible nonviscous fluids
Transport equations due to the non-Lipschitzian vector fields and fluid mechanics
Linear transport equations with initial values in Sobolev spaces and application to the Navier-Stokes equations
Über die Bewegung einer Flüssigkeit, die in ein seinen Ort änderndes Gefäß eingeschlossen ist.
Log-Lipschitz regularity and uniqueness of the flow for a field in \((W_{\text{loc}}^{n/p+1,p}(\mathbb{R}^n))^n\)
Persistence of the incompressible Euler equations in a Besov space \(\mathbf B_{1,1}^{d+1}(\mathbb R^d)\)
Ill-posedness for the incompressible Euler equations in critical Sobolev spaces
A quantitative theory for the continuity equation
Sobolev regular flows of non-Lipschitz vector fields
Orlicz spaces and generalized Orlicz spaces
Singular integrals and a problem on mixing flows
Über einige Existenzprobleme der Hydrodynamik. IV: Stetigkeitssätze. Eine Begründung der Helmholtz-Kirchhoffschen Theorie geradliniger Wirbelfäden.
Un théorème sur l'existence du mouvement plan d'un fluide parfait, homogene, incompressible, pendant un temps infiniment long
Über die unbeschränkte Fortsetzbarkeit einer stetigen ebenen Bewegung in einer unbegrenzten inkompressiblen Flüssigkeit
Remarks on the Euler equation
Sobolev estimates for solutions of the transport equation and ODE flows associated to non-Lipschitz drifts
Differentiability in measure of the flow associated with a nearly incompressible BV vector field
Sharp regularity estimates for solutions of the continuity equation drifted by Sobolev vector fields
A simple ill-posedness proof for incompressible Euler equations in critical Sobolev spaces
Small scale creation in active scalars
Loss of regularity for the 2D Euler equations
Loss of regularity for the continuity equation with non-Lipschitz velocity field
\(L^\infty\) ill-posedness for a class of equations arising in hydrodynamics
Quantitative regularity estimates for compressible transport equations
Convergence of numerical approximations to non-linear continuity equations with rough force fields
Strong illposedness of the incompressible Euler equation in integer \(C^m\) spaces
Estimates in Besov spaces for transport and transport-diffusion equations with almost Lipschitz coefficients
Renormalized solutions of some transport equations with partially \(W^{1,1}\) velocities and applications
A lemma and a conjecture on the cost of rearrangements
Strong ill-posedness of the incompressible Euler equation in borderline Sobolev spaces
Groups of diffeomorphisms and the motion of an incompressible fluid
Nonstationary flows of viscous and ideal fluids in \(R^3\)
\(H^p\) spaces of several variables
Vorticity and Incompressible Flow
Existence of Solution for the Euler Equations in a Critical Besov Space (ℝⁿ)
Estimates and regularity results for the DiPerna-Lions flow
Ill-posedness of the basic equations of fluid dynamics in Besov spaces
Continuity of the solution map of the Euler equations in Hölder spaces and weak norm inflation in Besov spaces
Incompressible flows of an ideal fluid with vorticity in borderline spaces of besov type1
Regularity estimates for the flow of BV autonomous divergence-free vector fields in R2
Strong Ill-Posedness of the 3D Incompressible Euler Equation in Borderline Spaces
Classical Fourier Analysis
Fractional Integration in Orlicz Spaces. I
Very weak notions of differentiability
On the Euler equations of incompressible fluids
Classical flows of vector fields with exponential or sub-exponential summability
Exponential Mixing by Shear Flows
Propagation of regularity for transport equations. A Littlewood-Paley approach
Instantaneous gap loss of Sobolev regularity for the 2D incompressible Euler equations

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