Duchon, Jean; Robert, Raoul Relaxation of Euler equations and hydrodynamic instabilities. (English) Zbl 0809.35080 Q. Appl. Math. 50, No. 2, 235-255 (1992). 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. Cited in 1 ReviewCited in 3 Documents MSC: 35Q35 PDEs in connection with fluid mechanics 76E99 Hydrodynamic stability 76B47 Vortex flows for incompressible inviscid fluids Keywords:vortex sheet dynamics; incompressible Euler equations; homogenization techniques PDFBibTeX XMLCite \textit{J. Duchon} and \textit{R. Robert}, Q. Appl. Math. 50, No. 2, 235--255 (1992; Zbl 0809.35080) Full Text: DOI