On a class of singular solutions to the incompressible 3-D Euler equation

2012/09/27 by Joerg Kampen, Kampen, Joerg · 1 citation
Earth and Planetary Sciences · Mathematics · #35Q31 #76N10 #Analysis of PDEs (math.AP) #Aquatic and Environmental Studies #Differential Equations and Numerical Methods #FOS: Mathematics #Navier-Stokes equation solutions

paper · pdf · doi:10.48550/arxiv.1209.6250

openalex publication_date 2012/09/27 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28

Abstract

A class of singular 3D-velocity vector fields is constructed which satisfy the incompressible 3D-Euler equation. It is shown that such a solution scheme does not exist in dimension 2. The solutions constructed are bounded and smooth up to finite time where they become singular. Although the solution is smooth and bounded there seems to be no bound in L2 of the velocity field.

Citations

• Sur le mouvement d'un liquide visqueux emplissant l'espace

Cited by

• On global schemes for highly degenerate Navier Stokes equation systems

Related

• A 3D Euler equation solution with 2D sets of singularities and data with\n Hoelder continuous first order derivatives
• An extension theorem for weak solutions of the 3d incompressible Euler equations and applications to singular flows
• Hölder Continuous Euler Flows in Three Dimensions with Compact Support in Time
• Finite-Time Singularity Formation for C^1,α Solutions to the Incompressible Euler Equations on ℝ³
• Finite time singularities to the 3D incompressible Euler equations for solutions in C^∞(ℝ³ ∖ \0\)∩ C^1,α∩ L²