Loss of continuity of the solution map for the Euler equations in $\alpha$-modulation and Hölder spaces

Abstract

We study the incompressible Euler equations in the $\alpha$-modulation $M_{p,q}^{s,\alpha }$ and Hölder $C^{1+\sigma }$ spaces on the plane. We show that for these spaces the associated data-to-solution map is not continuous on bounded sets.

References in corpus (1)

• Ill-posedness of the incompressible Euler equations in the $C^1$ space