chapter  21
8 Pages

Instability for Incompressible and Inviscid Fluids

ByH. Koch

We discuss well-posedness questions in C1,α in all dimensions. For two space dimensions it is shown that stability of a stationary solution in C1,α implies that all flow lines are periodic with a single (not necessarely minimal) period T. In particular all shear flows are unstable. Moreover the Fredholm spectrum of the linearized group is an annulus with radii determined by the stagnation points, provided stagnation points exist.