an:01801548
Zbl 1006.76008
Koch, Herbert
Transport and instability for perfect fluids
EN
Math. Ann. 323, No. 3, 491-523 (2002).
00086033
2002
j
76B03 76E30 35Q30
incompressible perfect fluids; Euler equations; well-posedness; nonlinear instability; transport techniques; large time behavior; linear stability
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.