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

Gerard Misio{\l}ek; Tsuyoshi Yoneda

arxiv: 1412.4619 · v1 · pith:MKWOHCOAnew · submitted 2014-12-15 · 🧮 math.AP

Loss of continuity of the solution map for the Euler equations in α-modulation and H\"older spaces

Gerard Misio{\l}ek , Tsuyoshi Yoneda This is my paper

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keywords alphaspacesequationseulermodulationolderassociatedbounded

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

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Loss of continuity of the solution map for the Euler equations in α-modulation and H\"older spaces

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