Lp-theory for incompressible Newtonian flows: energy preserving boundary conditions, weakly singular domains
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| Main Author: | |
|---|---|
| Format: | Thesis Book |
| Language: | English |
| Published: |
Wiesbaden
Springer Spektrum
2013
|
| Series: | Research
|
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XI, 183 S. graph. Darst. |
| ISBN: | 9783658010515 |
Staff View
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| 245 | 1 | 0 | |a Lp-theory for incompressible Newtonian flows |b energy preserving boundary conditions, weakly singular domains |c Matthias Köhne |
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Record in the Search Index
| _version_ | 1804150265909084160 |
|---|---|
| adam_text | IMAGE 1
CONTENTS
INTRODUCTION 1
ABSTRACT AND NOTATION 7
T H E MODEL
1 THE NAVIER-STOKES EQUATIONS 11
1.1 THE PRINCIPLES OF CONTINUUM MECHANICS 11
1.2 CONSERVATION OF MASS 14
1.3 CONSERVATION OF MOMENTUM 14
1.4 CONSTITUTIVE EQUATIONS 16
REMARKS 18
REFERENCES 18
2 ENERGY PRESERVING BOUNDARY CONDITIONS 2 1
2.1 GENERIC TRANSMISSION CONDITIONS 22
2.2 IMPERMEABLE WALLS 23
2.3 FREE SURFACES AND INTERFACES 24
2.4 ARTIFICIAL BOUNDARIES 25
2.5 ENERGY PRESERVING BOUNDARY CONDITIONS 25
2.6 VORTICITY AND PRESSURE BOUNDARY CONDITIONS 29
REMARKS 30
REFERENCES 31
BOUNDED SMOOTH DOMAINS
3 IP-THEORY FOR INCOMPRESSIBLE NEWTONIAN FLOWS 35
3.1 NECESSARY REGULARITY CONDITIONS 38
3.2 ADDITIONAL REGULARITY OF THE PRESSURE TRACE 43
3.3 NECESSARY COMPATIBILITY CONDITIONS 45
3.4 MAXIMAL L P-REGULARITY OF THE STOKES EQUATIONS 46
3.5 ASSOCIATED STOKES OPERATORS 48
3.6 WELL-POSEDNESS OF THE NAVIER-STOKES EQUATIONS 52
REMARKS 56
REFERENCES 61
HTTP://D-NB.INFO/1027235573
IMAGE 2
X C O N T E N T S
4 TOOLS AND METHODS 67
4.1 LP-THEORY FOR ELLIPTIC PROBLEMS 68
4.2 LP-THEORY FOR PARABOLIC PROBLEMS 74
4.3 SPECIAL SOLUTIONS IN A HALFSPACE 77
4.4 SECTORIAL OPERATORS AND FUNCTIONAL CALCULUS 83
4.5 A SPLITTING SCHEME FOR THE STOKES EQUATIONS 90
4.6 UNIFORM SOBOLEV TYPE EMBEDDINGS 94
REMARKS 97
REFERENCES 99
5 MAXIMAL L P-REGULARITY IN A HALFSPACE 101
5.1 STRATEGY 103
5.2 THE TRANSFORMED STOKES EQUATIONS 106
5.3 BOUNDARY CONDITIONS INVOLVING THE NORMAL VELOCITY 108
5.4 BOUNDARY CONDITIONS INVOLVING THE PRESSURE I L L
REMARKS 114
REFERENCES 114
6 MAXIMAL .LP-REGULARITY IN A BENT HALFSPACE 115
6.1 STRATEGY 117
6.2 TRANSFORMATION TO A HALFSPACE 120
6.3 BOUNDARY CONDITIONS INVOLVING THE NORMAL VELOCITY 124
6.4 BOUNDARY CONDITIONS INVOLVING THE PRESSURE 126
REMARKS 126
REFERENCES 126
7 MAXIMAL P-REGULARITY IN A BOUNDED SMOOTH DOMAIN 127
7.1 STRATEGY 129
7.2 PARTITION OF THE DOMAIN 131
7.3 THE REGULARITY OF THE PRESSURE 135
7.4 BOUNDARY CONDITIONS INVOLVING THE NORMAL VELOCITY 136
7.5 BOUNDARY CONDITIONS INVOLVING THE PRESSURE 143
REMARKS 150
REFERENCES 150
IMAGE 3
CONTENTS XI
BOUNDED WEAKLY SINGULAR DOMAINS
8 LP -THEORY IN WEAKLY SINGULAR DOMAINS 153
8.1 WEAKLY SINGULAR DOMAINS 154
8.2 NECESSARY REGULARITY CONDITIONS 158
8.3 NECESSARY COMPATIBILITY CONDITIONS 160
8.4 MAXIMAL L P-REGULARITY OF THE STOKES EQUATIONS 161
8.5 LP-THEORY FOR ELLIPTIC PROBLEMS 162
8.6 LP-THEORY FOR PARABOLIC PROBLEMS 164
8.7 THE REFLECTION METHOD 164
REMARKS 166
REFERENCES 166
BIBLIOGRAPHY 169
TABLE OF SYMBOLS 175
. INDEX 181
|
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| illustrated | Illustrated |
| indexdate | 2024-07-10T00:36:11Z |
| institution | BVB |
| isbn | 9783658010515 |
| language | English |
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| physical | XI, 183 S. graph. Darst. |
| publishDate | 2013 |
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| publisher | Springer Spektrum |
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| spelling | Köhne, Matthias Verfasser aut Lp-theory for incompressible Newtonian flows energy preserving boundary conditions, weakly singular domains Matthias Köhne Wiesbaden Springer Spektrum 2013 XI, 183 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Research Zugl.: Darmstadt, Techn. Univ., Diss., 2011 Lp-Raum (DE-588)4168195-2 gnd rswk-swf Inkompressibles Fluid (DE-588)4774172-7 gnd rswk-swf Newtonsche Flüssigkeit (DE-588)4191473-9 gnd rswk-swf (DE-588)4113937-9 Hochschulschrift gnd-content Newtonsche Flüssigkeit (DE-588)4191473-9 s Inkompressibles Fluid (DE-588)4774172-7 s Lp-Raum (DE-588)4168195-2 s DE-604 DNB Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=025935516&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Köhne, Matthias Lp-theory for incompressible Newtonian flows energy preserving boundary conditions, weakly singular domains Lp-Raum (DE-588)4168195-2 gnd Inkompressibles Fluid (DE-588)4774172-7 gnd Newtonsche Flüssigkeit (DE-588)4191473-9 gnd |
| subject_GND | (DE-588)4168195-2 (DE-588)4774172-7 (DE-588)4191473-9 (DE-588)4113937-9 |
| title | Lp-theory for incompressible Newtonian flows energy preserving boundary conditions, weakly singular domains |
| title_auth | Lp-theory for incompressible Newtonian flows energy preserving boundary conditions, weakly singular domains |
| title_exact_search | Lp-theory for incompressible Newtonian flows energy preserving boundary conditions, weakly singular domains |
| title_full | Lp-theory for incompressible Newtonian flows energy preserving boundary conditions, weakly singular domains Matthias Köhne |
| title_fullStr | Lp-theory for incompressible Newtonian flows energy preserving boundary conditions, weakly singular domains Matthias Köhne |
| title_full_unstemmed | Lp-theory for incompressible Newtonian flows energy preserving boundary conditions, weakly singular domains Matthias Köhne |
| title_short | Lp-theory for incompressible Newtonian flows |
| title_sort | lp theory for incompressible newtonian flows energy preserving boundary conditions weakly singular domains |
| title_sub | energy preserving boundary conditions, weakly singular domains |
| topic | Lp-Raum (DE-588)4168195-2 gnd Inkompressibles Fluid (DE-588)4774172-7 gnd Newtonsche Flüssigkeit (DE-588)4191473-9 gnd |
| topic_facet | Lp-Raum Inkompressibles Fluid Newtonsche Flüssigkeit Hochschulschrift |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=025935516&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT kohnematthias lptheoryforincompressiblenewtonianflowsenergypreservingboundaryconditionsweaklysingulardomains |