The wellposedness of twodimensional ideal flow
Abstract
The existence, uniqueness, and regularity of solutions to the Euler equations applied to modelling twodimensional flows is demonstrated. An elementary proof of the existence of regular solutions is presented, and consideration is given to the Euler equation with singular conditions, e.g., the KelvinHelmholtz instability featuring an initial velocity discontinuous across a vortex sheet. The Fourier transform of the sheet and the vorticity density are shown to decay exponentially at large wavenumbers by an example of the stability of a stationary solution of the Euler equation, where the velocity is constant in two regions separated by a straight line of discontinuity.
 Publication:

Journal de Mecanique Theorique et Appliquee Supplement
 Pub Date:
 1983
 Bibcode:
 1983JMTAS......217S
 Keywords:

 Euler Equations Of Motion;
 Flow Equations;
 Flow Theory;
 Ideal Fluids;
 Two Dimensional Flow;
 Vorticity;
 Existence Theorems;
 KelvinHelmholtz Instability;
 Singularity (Mathematics);
 Vortex Sheets;
 Fluid Mechanics and Heat Transfer