Continuity Properties of the Solution Map for the Euler–Poisson Equation

Continuity Properties of the Solution Map for the Euler–Poisson Equation

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 γ topology for s...

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Veröffentlicht in:Journal of mathematical fluid mechanics 2018-06, Vol.20 (2), p.757-769
Hauptverfasser: Holmes, J., Tığlay, F.
Format: Artikel
Sprache:eng
Schlagworte:
Classical and Continuum Physics
Fluid mechanics
Fluid- and Aerodynamics
Mathematical Methods in Physics
Physics
Physics and Astronomy
Poisson equation
Sobolev space
Theoretical mathematics
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Zusammenfassung: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 γ topology for s > γ and find that the data-to-solution map is Hölder continuous.
ISSN:1422-6928
1422-6952
DOI:10.1007/s00021-017-0343-4