# 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 $$H^s$$ 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. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Journal of Mathematical Fluid Mechanics Springer Journals

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

, Volume 20 (2) – Nov 2, 2017
13 pages

/lp/springer_journal/continuity-properties-of-the-solution-map-for-the-euler-poisson-6Ztn85OnIH
Publisher
Springer International Publishing
Subject
Physics; Fluid- and Aerodynamics; Mathematical Methods in Physics; Classical and Continuum Physics
ISSN
1422-6928
eISSN
1422-6952
D.O.I.
10.1007/s00021-017-0343-4
Publisher site
See Article on Publisher Site

### 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 $$H^s$$ 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

Journal of Mathematical Fluid MechanicsSpringer Journals

Published: Nov 2, 2017

## You’re reading a free preview. Subscribe to read the entire article.

### DeepDyve is your personal research library

It’s your single place to instantly
that matters to you.

over 18 million articles from more than
15,000 peer-reviewed journals.

All for just $49/month ### Explore the DeepDyve Library ### Search Query the DeepDyve database, plus search all of PubMed and Google Scholar seamlessly ### Organize Save any article or search result from DeepDyve, PubMed, and Google Scholar... all in one place. ### Access Get unlimited, online access to over 18 million full-text articles from more than 15,000 scientific journals. ### Your journals are on DeepDyve Read from thousands of the leading scholarly journals from SpringerNature, Elsevier, Wiley-Blackwell, Oxford University Press and more. All the latest content is available, no embargo periods. DeepDyve ### Freelancer DeepDyve ### Pro Price FREE$49/month
\$360/year

Save searches from
PubMed

Create lists to

Export lists, citations