Convergence of filtered weak solutions to the 2D Euler equations with measure-valued vorticity

DOI10.1007/s00028-020-00563-4zbMath1464.35198arXiv1810.09636OpenAlexW3105405056MaRDI QIDQ2021533

Takeshi Gotoda

Publication date: 27 April 2021

Published in: Journal of Evolution Equations (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1810.09636

zbMATH Keywords

global weak solutionRadon measureinviscid Euler equationsvortex sheet solutions

Mathematics Subject Classification ID

Smoothness and regularity of solutions to PDEs (35B65) Vortex flows for incompressible inviscid fluids (76B47) Existence problems for PDEs: global existence, local existence, non-existence (35A01) Weak solutions to PDEs (35D30) Euler equations (35Q31) Uniqueness problems for PDEs: global uniqueness, local uniqueness, non-uniqueness (35A02) PDEs with measure (35R06)

Related Items

Energy conservation in the limit of filtered solutions for the 2D Euler equations ⋮ The Limit $\alpha \to 0$ of the $\alpha$-Euler Equations in the Half-Plane with No-Slip Boundary Conditions and Vortex Sheet Initial Data

Cites Work

• Unnamed Item
• Unnamed Item
• Interaction of vortices in weakly viscous planar flows
• On the global evolution of vortex filaments, blobs, and small loops in 3D ideal flows
• Direct numerical simulations of the Navier-Stokes alpha model
• A vortex method for flows with slight density variations
• 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
• The Euler-Poincaré equations and semidirect products with applications to continuum theories
• Mathematical theory of incompressible nonviscous fluids
• The anisotropic Lagrangian averaged Euler and Navier-Stokes equations
• Global solvability for two-dimensional filtered Euler equations with measure valued initial vorticity.
• Discretization of a vortex sheet with an example of roll-up
• Nonstationary plane flow of viscous and ideal fluids
• THE VORTEX BLOB METHOD AS A SECOND-GRADE NON-NEWTONIAN FLUID
• A study of the Navier–Stokes-α model for two-dimensional turbulence
• Diffraction of a weak shock with vortex generation
• A criterion for the equivalence of the Birkhoff-Rott and Euler descriptions of vortex sheet evolution
• Numerical simulations of the Lagrangian averaged Navier–Stokes equations for homogeneous isotropic turbulence
• Global regularity and convergence of a Birkhoff-Rott-α approximation of the dynamics of vortex sheets of the two-dimensional Euler equations
• A study of singularity formation in a vortex sheet by the point-vortex approximation
• Long time existence for a slightly perturbed vortex sheet
• Analytic structure of vortex sheet dynamics. Part 1. Kelvin–Helmholtz instability
• Existence de Nappes de Tourbillon en Dimension Deux
• Motion of three vortices
• The spontaneous appearance of a singularity in the shape of an evolving vortex sheet
• Camassa-Holm Equations as a Closure Model for Turbulent Channel and Pipe Flow
• Universality of the Anomalous Enstrophy Dissipation at the Collapse of Three Point Vortices on Euler--Poincaré Models
• Concentrations in regularizations for 2‐D incompressible flow
• 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
• Euler-alpha and vortex blob regularization of vortex filament and vortex sheet motion
• Non-stationary flow of an ideal incompressible liquid
• A numerical study of vortex ring formation at the edge of a circular tube
• The \(N\)-vortex problem. Analytical techniques
• The Navier-Stokes-alpha model of fluid turbulence
• The three dimensional viscous Camassa-Holm equations, and their relation to the Navier-Stokes equations and turbulence theory

This page was built for publication: Convergence of filtered weak solutions to the 2D Euler equations with measure-valued vorticity