×

Relaxation of Euler equations and hydrodynamic instabilities. (English) Zbl 0809.35080

In order to understand vortex sheet dynamics, the authors consider the Cauchy problem modeling an incompressible perfect fluid; in fact they introduce and study a relaxed version of the incompressible Euler equations. Using homogenization techniques they establish a system of equations governing foliated flows involving two velocities (measure- valued solutions). These flows have a microstructure; namely, the flow is organized in thin sheets which are free to slide one over the other. These relaxed equations admit interesting solutions. The authors give three examples of such solutions (foliated flows) and discuss their relevance and some physical and philosophical implications.

MSC:

35Q35 PDEs in connection with fluid mechanics
76E99 Hydrodynamic stability
76B47 Vortex flows for incompressible inviscid fluids
PDFBibTeX XMLCite
Full Text: DOI