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 |
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| container_end_page | 769 |
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| container_issue | 2 |
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| container_title | Journal of mathematical fluid mechanics |
| container_volume | 20 |
| creator | Holmes, J. Tığlay, F. |
| description | 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. |
| doi_str_mv | 10.1007/s00021-017-0343-4 |
| format | Article |
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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.</description><identifier>ISSN: 1422-6928</identifier><identifier>EISSN: 1422-6952</identifier><identifier>DOI: 10.1007/s00021-017-0343-4</identifier><language>eng</language><publisher>Cham: Springer International Publishing</publisher><subject>Classical and Continuum Physics ; Fluid mechanics ; Fluid- and Aerodynamics ; Mathematical Methods in Physics ; Physics ; Physics and Astronomy ; Poisson equation ; Sobolev space ; Theoretical mathematics</subject><ispartof>Journal of mathematical fluid mechanics, 2018-06, Vol.20 (2), p.757-769</ispartof><rights>Springer International Publishing AG 2017</rights><rights>Copyright Springer Science & Business Media 2018</rights><lds50>peer_reviewed</lds50><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c316t-365cb47950c22bf7be95c8f156d26b6c10180557687de7e28556cab120b939b23</citedby><cites>FETCH-LOGICAL-c316t-365cb47950c22bf7be95c8f156d26b6c10180557687de7e28556cab120b939b23</cites></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktopdf>$$Uhttps://link.springer.com/content/pdf/10.1007/s00021-017-0343-4$$EPDF$$P50$$Gspringer$$H</linktopdf><linktohtml>$$Uhttps://link.springer.com/10.1007/s00021-017-0343-4$$EHTML$$P50$$Gspringer$$H</linktohtml><link.rule.ids>314,777,781,27905,27906,41469,42538,51300</link.rule.ids></links><search><creatorcontrib>Holmes, J.</creatorcontrib><creatorcontrib>Tığlay, F.</creatorcontrib><title>Continuity Properties of the Solution Map for the Euler–Poisson Equation</title><title>Journal of mathematical fluid mechanics</title><addtitle>J. Math. Fluid Mech</addtitle><description>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.</description><subject>Classical and Continuum Physics</subject><subject>Fluid mechanics</subject><subject>Fluid- and Aerodynamics</subject><subject>Mathematical Methods in Physics</subject><subject>Physics</subject><subject>Physics and Astronomy</subject><subject>Poisson equation</subject><subject>Sobolev space</subject><subject>Theoretical mathematics</subject><issn>1422-6928</issn><issn>1422-6952</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2018</creationdate><recordtype>article</recordtype><recordid>eNp1kE1OwzAQRi0EEqVwAHaRWBvGTmzHS1SVPxVRCVhbsetAqhKntrPojjtwQ06CQxCsWM1o5n0z0kPolMA5ARAXAQAowUAEhrzIcbGHJqSgFHPJ6P5vT8tDdBTCGhLIJJ2gu5lrY9P2TdxlS-8662NjQ-bqLL7a7NFt-ti4Nruvuqx2_ns47zfWf75_LF0TQtrNt301QMfooK42wZ781Cl6vpo_zW7w4uH6dna5wCYnPOKcM6MLIRkYSnUttJXMlDVhfEW55oYAKYExwUuxssLSkjFuKk0oaJlLTfMpOhvvdt5texuiWrvet-mlolCUXCYfLFFkpIx3IXhbq843b5XfKQJqUKZGZSqZUIMyVaQMHTMhse2L9X-X_w99ATkfbiU</recordid><startdate>20180601</startdate><enddate>20180601</enddate><creator>Holmes, J.</creator><creator>Tığlay, F.</creator><general>Springer International Publishing</general><general>Springer Nature B.V</general><scope>AAYXX</scope><scope>CITATION</scope></search><sort><creationdate>20180601</creationdate><title>Continuity Properties of the Solution Map for the Euler–Poisson Equation</title><author>Holmes, J. ; Tığlay, F.</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c316t-365cb47950c22bf7be95c8f156d26b6c10180557687de7e28556cab120b939b23</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2018</creationdate><topic>Classical and Continuum Physics</topic><topic>Fluid mechanics</topic><topic>Fluid- and Aerodynamics</topic><topic>Mathematical Methods in Physics</topic><topic>Physics</topic><topic>Physics and Astronomy</topic><topic>Poisson equation</topic><topic>Sobolev space</topic><topic>Theoretical mathematics</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Holmes, J.</creatorcontrib><creatorcontrib>Tığlay, F.</creatorcontrib><collection>CrossRef</collection><jtitle>Journal of mathematical fluid mechanics</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Holmes, J.</au><au>Tığlay, F.</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Continuity Properties of the Solution Map for the Euler–Poisson Equation</atitle><jtitle>Journal of mathematical fluid mechanics</jtitle><stitle>J. Math. Fluid Mech</stitle><date>2018-06-01</date><risdate>2018</risdate><volume>20</volume><issue>2</issue><spage>757</spage><epage>769</epage><pages>757-769</pages><issn>1422-6928</issn><eissn>1422-6952</eissn><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
γ
topology for
s
>
γ
and find that the data-to-solution map is Hölder continuous.</abstract><cop>Cham</cop><pub>Springer International Publishing</pub><doi>10.1007/s00021-017-0343-4</doi><tpages>13</tpages></addata></record> |
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| language | eng |
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| subjects | Classical and Continuum Physics Fluid mechanics Fluid- and Aerodynamics Mathematical Methods in Physics Physics Physics and Astronomy Poisson equation Sobolev space Theoretical mathematics |
| title | Continuity Properties of the Solution Map for the Euler–Poisson Equation |
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