We study the continuity properties of the data-to-solution map for the modified Euler–Poisson equation. We show that for initial data in the Sobolev space $$H^s$$ H s , $$s>3/2$$ s > 3 / 2 , the data-to-solution map is not better than continuous. Furthermore, we consider the solution map in the $$H^\gamma $$ H γ topology for $$s>\gamma $$ s > γ and find that the data-to-solution map is Hölder continuous.
Journal of Mathematical Fluid Mechanics – Springer Journals
Published: Nov 2, 2017
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