×

zbMATH — the first resource for mathematics

Transport and instability for perfect fluids. (English) Zbl 1006.76008
Summary: Incompressible perfect fluids are described by Euler equations. We provide a new proof of well-posedness for velocities in \(C^{1,\alpha}\), and give linear and nonlinear instability results using transport techniques. The results have an important consequence: the topology of \(C^{1,\alpha}\) is too fine for interesting questions about large time behavior.

MSC:
76B03 Existence, uniqueness, and regularity theory for incompressible inviscid fluids
76E30 Nonlinear effects in hydrodynamic stability
35Q30 Navier-Stokes equations
PDF BibTeX XML Cite
Full Text: DOI