48 citations · 201 across the 22 of their papers we have counts for
19 papers · 1 filter
Non Uniqueness of power-law flows
Jan Burczak, Stefano Modena, László Székelyhidi
We apply the technique of convex integration to obtain non-uniqueness and existence results for power-law fluids, in dimension . For the power index below the compactne…
Mixing solutions for the Muskat problem with variable speed
Florent Noisette, László Székelyhidi
We provide a quick proof of the existence of mixing weak solutions for the Muskat problem with variable mixing speed. Our proof is considerably shorter and extends previous results…
Dissipative Euler flows for vortex sheet initial data without distinguished sign
Francisco Mengual, László Székelyhidi
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 sim…
A new approach to the Rayleigh-Taylor instability
Björn Gebhard, József J. Kolumbán, László Székelyhidi
In this article we consider the inhomogeneous incompressible Euler equations describing two fluids with different constant densities under the influence of gravity as a differentia…
Bounded solutions of ideal MHD with compact support in space-time
Daniel Faraco, Sauli Lindberg, László Székelyhidi
We show that in 3-dimensional ideal magnetohydrodynamics there exist infinitely many bounded solutions that are compactly supported in space-time and have non-trivial velocity and…
On turbulence and geometry: from Nash to Onsager
camillo De Lellis, László Székelyhidi
This article is a short nontechnical survey of recent progresses in fluid dynamics and differential geometry, relating a conjecture of Lars Onsager to the work of Nash on isometric…
Non-renormalized solutions to the continuity equation
Stefano Modena, László Székelyhidi
We show that there are continuous, (), incompressible vector fields for which uniqueness of solutions to the continuity equation fails.
Onsager's conjecture for admissible weak solutions
Tristan Buckmaster, Camillo De Lellis, László Székelyhidi +1
We prove that given any , a time interval , and given any smooth energy profile , there exists a weak solution of the three-dimensi…
High dimensionality and h-principle in PDE
Camillo De Lellis, László Székelyhidi
In this note we would like to present "an analysts' point of view" on the Nash-Kuiper theorem and in particular highlight the very close connection to some aspects of turbulence --…
Dissipative Euler flows with Onsager-critical spatial regularity
Tristan Buckmaster, Camillo De Lellis, László Székelyhidi
For any we show the existence of continuous periodic weak solutions of the Euler equations which do not conserve the kinetic energy and belong to the space $L^1_t (C_x^{\…
Weak solutions to the stationary incompressible Euler equations
Antoine Choffrut, László Székelyhidi
We consider weak stationary solutions to the incompressible Euler equations and show that the analogue of the h-principle obtained in [5, 7] for time-dependent weak solutions conti…
Transporting microstructure and dissipative Euler flows
Tristan Buckmaster, Camillo De Lellis, László Székelyhidi
Recently the second and third author developed an iterative scheme for obtaining rough solutions of the 3D incompressible Euler equations in Hölder spaces (arXiv:1202.1751 and arXi…
Dissipative Euler Flows and Onsager's Conjecture
Camillo De Lellis, László Székelyhidi
For any θ<1/10 we construct periodic weak solutions of the incompressible Euler equations which dissipate the total kinetic energy and are Hölder-continuous with exponent θ. A famo…
Dissipative continuous Euler flows in two and three dimensions
Antoine Choffrut, Camillo De Lellis, László Székelyhidi
Recently, two of these authors construct dissipative continuous (weak) solutions to the incompressible Euler equations on the three-dimensional torus . The building bl…
The -principle and the equations of fluid dynamics
Camillo De Lellis, László Székelyhidi
In this note we survey some recent results for the Euler equations in compressible and incompressible fluid dynamics. The main point of all these theorems is the surprising fact th…
The Operator Norm of a Quadratic Perturbation of the Real Part of the Ahlfors--Beurling Operator
Nicholas Boros, László Székelyhidi, 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…
Relaxation of the incompressible porous media equation
László Székelyhidi
It was shown recently by Cordoba, Faraco and Gancedo that the 2D porous media equation admits weak solutions with compact support in time. The proof, based on the convex integratio…
Uniqueness of normalized homeomorphic solutions to nonlinear Beltrami equations
Kari Astala, Albert Clop, Daniel Faraco +2
We settle the problem of the uniqueness of normalized homeomorphic solutions to nonlinear Beltrami equations . It turns out that the uniquene…
The Euler equations as a differential inclusion
Camillo De Lellis, László Székelyhidi
In this paper we propose a new point of view on weak solutions of the Euler equations, describing the motion of an ideal incompressible fluid in with . We g…