Abstract
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 \(H^s\), \(s>3/2\), the data-to-solution map is not better than continuous. Furthermore, we consider the solution map in the \(H^\gamma \) topology for \(s>\gamma \) and find that the data-to-solution map is Holder continuous.
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