Dissipative Euler Flows for Vortex Sheet Initial Data without Distinguished Sign

DOI10.1002/cpa.22038arXiv2005.08333OpenAlexW3024260950MaRDI QIDQ6139110

László jun. Székelyhidi, Francisco Mengual

Publication date: 16 January 2024

Published in: Communications on Pure and Applied Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2005.08333

Mathematics Subject Classification ID

Fluid mechanics (76-XX) Partial differential equations (35-XX)

Related Items

Linear instability of symmetric logarithmic spiral vortex sheets

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Dissipative continuous Euler flows
• On the energy dissipation rate of solutions to the compressible isentropic Euler system
• Non-uniqueness and \(h\)-principle for Hölder-continuous weak solutions of the Euler equations
• Weak-strong uniqueness for measure-valued solutions
• Weak solutions to the incompressible Euler equations with vortex sheet initial data
• On admissibility criteria for weak solutions of the Euler equations
• The Euler equations as a differential inclusion
• Desingularization of periodic vortex sheet roll-up
• Global vortex sheet solutions of Euler equations in the plane
• Finite time analyticity for the two and three dimensional Kelvin- Helmholtz instability
• On \(L^ 1\)-vorticity for 2-D incompressible flow
• Onsager's conjecture on the energy conservation for solutions of Euler's equation
• Energy dissipation without viscosity in ideal hydrodynamics. I: Fourier analysis and local energy transfer
• A proof of Onsager's conjecture
• The Riemann problem for the multidimensional isentropic system of gas dynamics is ill-posed if it contains a shock
• Degraded mixing solutions for the Muskat problem
• Piecewise constant subsolutions for the Muskat problem
• A new approach to the Rayleigh-Taylor instability
• Mixing solutions for the Muskat problem
• Maximal dissipation and well-posedness for the compressible Euler system
• Young measures generated by ideal incompressible fluid flows
• The entropy rate admissibility criterion for solutions of hyperbolic conservation laws
• Vorticity and Incompressible Flow
• A naive parametrization for the vortex-sheet problem
• High dimensionality and h-principle in PDE
• Onsager's Conjecture for Admissible Weak Solutions
• A criterion for the equivalence of the Birkhoff-Rott and Euler descriptions of vortex sheet evolution
• Singular Solutions and Ill-Posedness for the Evolution of Vortex Sheets
• Convergence of the Vortex Method for Vortex Sheets
• Existence de Nappes de Tourbillon en Dimension Deux
• The spontaneous appearance of a singularity in the shape of an evolving vortex sheet
• Hardy Spaces and the Two-Dimensional Euler Equations with Nonnegative Vorticity
• Relaxation of the incompressible porous media equation
• Ill-posedness of the rayleigh-taylor and helmholtz problems for incompressible fluids
• Inertial energy dissipation for weak solutions of incompressible Euler and Navier-Stokes equations
• The weak vorticity formulation of the 2-d euler equations and concentration-cancellation
• Convergence of vortex methods for weak solutions to the 2‐D euler equations with vortex sheet data
• The point-vortex method for periodic weak solutions of the 2-D Euler equations
• The ℎ-principle and the equations of fluid dynamics
• Vortex Layers of Small Thickness
• Global Ill‐Posedness of the Isentropic System of Gas Dynamics
• Mathematical analysis of vortex sheets
• Existence of vortex sheets with reflection symmetry in two space dimensions.