526 citations · 1.1k across the 12 of their papers we have counts for
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Non-uniqueness for the Euler equations up to Onsager's critical exponent
Sara Daneri, Eris Runa, Laszlo Szekelyhidi
In this paper we deal with the Cauchy problem for the incompressible Euler equations in the three-dimensional periodic setting. We prove non-uniqueness for an -dense set of Hö…
Very weak solutions to the two dimensional Monge-Ampére equation
Wentao Cao, László Székelyhidi
In this short note we revisit the convex integration approach to constructing very weak solutions to the 2D Monge-Ampére equation with Hölder-continuous first derivatives of expone…
Non-uniqueness for the transport equation with Sobolev vector fields
Stefano Modena, László Székelyhidi
We construct a large class of examples of non-uniqueness for the linear transport equation and the transport-diffusion equation with divergence-free vector fields in Sobolev spaces…
Piecewise constant subsolutions for the Muskat problem
Clemens Förster, László Székelyhidi
We show the existence of infinitely many admissible weak solutions for the incompressible porous media equations for all Muskat-type initial data with -regularity of the i…
Non-uniqueness and h-principle for Hölder-continuous weak solutions of the Euler equations
Sara Daneri, László Székelyhidi
In this paper we address the Cauchy problem for the incompressible Euler equations in the periodic setting. Based on estimates developed in [Buckmaster-De Lellis-Isett-Székelyhidi]…
Equidimensional isometric maps
Bernd Kirchheim, Emanuele Spadaro, Laszlo Szekelyhidi
In Gromov's treatise Partial Differential Relations (volume 9 of Ergebnisse der Mathematik und ihrer Grenzgebiete (3), 1986), a continuous map between Riemannian manifolds is calle…
Dissipative continuous Euler flows
Camillo De Lellis, László Székelyhidi
We show the existence of continuous periodic solutions of the 3D incompressible Euler equations which dissipate the total kinetic energy.
Laminates Meet Burkholder Functions
Nicholas Boros, Laszlo Szekelyhidi, Alexander Volberg
We will explain how to compute the exact operator norm of a "quadratic perturbation" of the real part of the Ahlfors--Beurling operator. For the lower bound estimate we use a…
Young Measures Generated by Ideal Incompressible Fluid Flows
László Székelyhidi, Emil Wiedemann
In their seminal paper "Oscillations and concentrations in weak solutions of the incompressible fluid equations", R. DiPerna and A. Majda introduced the notion of measure-valued so…
Weak-strong uniqueness for measure-valued solutions
Yann Brenier, Camillo De Lellis, László Székelyhidi
We prove the weak-strong uniqueness for measure-valued solutions of the incompressible Euler equations. These were introduced by R.DiPerna and A.Majda, and in particular global exi…
On admissibility criteria for weak solutions of the Euler equations
Camillo De Lellis, László Székelyhidi
We consider solutions to the Cauchy problem for the incompressible Euler equations satisfying several additional requirements, like the global and local energy inequalities. Using…