zbMATH — the first resource for mathematics

Concentration sets for 2D incompressible flow. (English) Zbl 0888.76013
Summary: We recall the definition of DiPerna-Majda concentration sets and their role in the study of existence for the incompressible 2D Euler equations with singular initial data. We review examples of concentration-cancellation, focusing on the issue of dynamic kinetic energy defects for the limit flows. We also describe a recent refined estimate of the dimension of (sequential) concentrations which depends on additional temporal regularity. Finally, we discuss the possibility of obtaining the temporal regularity a priori for smooth solutions, and a related problem of controlling the evolution of the support of vorticity.
76B99 Incompressible inviscid fluids
35Q35 PDEs in connection with fluid mechanics
PDF BibTeX Cite