Critical functional framework and maximal regularity in action on systems of incompressible flows:
Gespeichert in:
| Hauptverfasser: | , |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Paris
Société Mathématique de France
2015
|
| Schriftenreihe: | Mémoires de la SMF
143 |
| Schlagworte: | |
| Online-Zugang: | Klappentext Inhaltsverzeichnis |
| Beschreibung: | VI, 151 Seiten |
| ISBN: | 9782856298244 |
Internformat
MARC
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| 245 | 1 | 0 | |a Critical functional framework and maximal regularity in action on systems of incompressible flows |c Raphaël Danchin, Piotr Bogusław Mucha |
| 264 | 1 | |a Paris |b Société Mathématique de France |c 2015 | |
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Datensatz im Suchindex
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|---|---|
| adam_text | This memoir is devoted to endpoint maximal regularity in Besov spaces
for the evolutionary Stokes system in bounded or exterior domains of Mn.
We strive for time independent a priori estimates with L time integra-
bility.
In the whole space case, endpoint maximal regularity estimates are
well known and have proved to be spectacularly powerful to investigate
the well-posedness issue of PDEs related to fluid mechanics. They have
been extended recently by the authors to the half-space setting [15].
The present work deals with the bounded and exterior domain cases.
Although in both situations the Stokes system may be localized and
reduced up to low order terms to the half-space and whole space cases,
the exterior domain case is more involved owing to a bad control on
the low frequencies of the solution (no Poincare inequality is available
whatsoever). In order to glean some global-in-time integrability, we adapt
to the Besov space setting the approach introduced by P. Maremonti
and V.A. Solonnikov in [39]. The price to pay is that We end up with
estimates in intersections of Besov spaces, rather than in a single Besov
space.
As a first application of our work, we solve locally for large data or glob-
ally for small data, the (slightly) inhomogeneous incompressible Navier-
Stokes equations in critical Besov spaces, in an exterior domain. After
observing that the L time integrability allows to determine globally the
streamlines of the flow, the whole system is recast in the Lagrangian coor-
dinates setting. This, in particular, enables us to consider discontinuous
densities, as in |17|, |19|.
The second application concerns a low Mach number system that has
been studied recently in the whole space setting by the first author and
X. Liao [14].
Société
Mathématique
de France
Imprimerie Sepec o 1960 Péronnas - France
Dépôt légal . décembre 2015 - № N04615151 106
ISBN 978-2-85629-824-
9
ISSN 0249-633-Х
CONTENTS
F9
1. Introduction ...................................................... 1
2. Tools and spaces .................................................. 9
2.1. Besov spaces on M” .......................................... 9
2.2. Besov spaces on domains ..................................... 18
2.3. The divergence equation ..................................... 24
2.4. Change of coordinates ....................................... 27
3. The Poisson equation ............................................. 33
3.1. The whole space case ........................................ 33
3.2. The homogeneous Neumann problem in bounded domains........... 35
3.3. The half-space case ......................................... 43
3.4. The Neumann problem in bounded or exterior domains .......... 50
3.5. Helmholtz projection ........................................ 59
4. The evolutionary Stokes system ................................... 61
4.1. The whole space case ........................................ 61
4.2. The Stokes system in the half-space ......................... 64
4.3. The exterior domain case .................................... 72
5. Inhomogeneous Navier-Stokes equations in exterior domains 97
5.1. Lagrangian stream lines setting ............................. 98
5.2. The linearized equations .................................... 99
5.3. Local-in-time existence .....................................107
5.4. Global in time existence ....................................114
5.5. Estimates of nonlinearities .................................119
vi
CONTENTS
6. The low Mach number system .................................123
6.1. The system ..............................................123
6.2. The heat equation with Neumann boundary conditions......125
6.3. Solving a low Mach number system ........................139
Bibliography ...................................................147
MEMOIRES DE LA SMF 143
|
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| id | DE-604.BV043339971 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-10T07:23:28Z |
| institution | BVB |
| isbn | 9782856298244 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-028759916 |
| oclc_num | 936603833 |
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| physical | VI, 151 Seiten |
| publishDate | 2015 |
| publishDateSearch | 2015 |
| publishDateSort | 2015 |
| publisher | Société Mathématique de France |
| record_format | marc |
| series | Mémoires de la SMF |
| series2 | Mémoires de la SMF |
| spelling | Danchin, Raphaël 1971- Verfasser (DE-588)143364286 aut Critical functional framework and maximal regularity in action on systems of incompressible flows Raphaël Danchin, Piotr Bogusław Mucha Paris Société Mathématique de France 2015 VI, 151 Seiten txt rdacontent n rdamedia nc rdacarrier Mémoires de la SMF 143 Differentialoperator (DE-588)4012251-7 gnd rswk-swf D-Modul (DE-588)4305548-5 gnd rswk-swf Differentialoperator (DE-588)4012251-7 s D-Modul (DE-588)4305548-5 s 1\p DE-604 Mucha, Piotr Verfasser aut Mémoires de la SMF 143 (DE-604)BV000000921 143 Digitalisierung UB Bayreuth - ADAM Catalogue Enrichment application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=028759916&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Klappentext Digitalisierung UB Bayreuth - ADAM Catalogue Enrichment application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=028759916&sequence=000002&line_number=0002&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Danchin, Raphaël 1971- Mucha, Piotr Critical functional framework and maximal regularity in action on systems of incompressible flows Mémoires de la SMF Differentialoperator (DE-588)4012251-7 gnd D-Modul (DE-588)4305548-5 gnd |
| subject_GND | (DE-588)4012251-7 (DE-588)4305548-5 |
| title | Critical functional framework and maximal regularity in action on systems of incompressible flows |
| title_auth | Critical functional framework and maximal regularity in action on systems of incompressible flows |
| title_exact_search | Critical functional framework and maximal regularity in action on systems of incompressible flows |
| title_full | Critical functional framework and maximal regularity in action on systems of incompressible flows Raphaël Danchin, Piotr Bogusław Mucha |
| title_fullStr | Critical functional framework and maximal regularity in action on systems of incompressible flows Raphaël Danchin, Piotr Bogusław Mucha |
| title_full_unstemmed | Critical functional framework and maximal regularity in action on systems of incompressible flows Raphaël Danchin, Piotr Bogusław Mucha |
| title_short | Critical functional framework and maximal regularity in action on systems of incompressible flows |
| title_sort | critical functional framework and maximal regularity in action on systems of incompressible flows |
| topic | Differentialoperator (DE-588)4012251-7 gnd D-Modul (DE-588)4305548-5 gnd |
| topic_facet | Differentialoperator D-Modul |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=028759916&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=028759916&sequence=000002&line_number=0002&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV000000921 |
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