Navier-Stokes equations in irregular domains:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English Russian |
| Published: |
Dordrecht u.a.
Kluwer
1995
|
| Series: | Mathematics and its applications
326 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XV, 566 S. |
| ISBN: | 0792335090 |
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Record in the Search Index
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| adam_text | NAVIER-STOKES EQUATIONS IN IRREGULAR DOMAINS BY L. STUPELIS INSTITUTE OF
MATHEMATICS AND INFORMATICS, VILNIUS, LITHUANIA KLUWER ACADEMIC
PUBLISHERS DORDRECHT / BOSTON / LONDON CONTENTS PREFACE XIII CHAPTER 1.
PRELIMINARIES 1 1.1. NORMED LINEAR SPACES AND OPERATORS 1 1.1.1. NORMED
LINEAR SPACES 1 1.1.2. LINEAR OPERATORS 5 1.1.3. REGULARIZATION OF
OPERATORS 10 1.2. SOME FUNCTIONAL SPACES 11 1.2.1. SPACES OF GENERALIZED
FUNCTIONS 11 1.2.2. INEQUALITIES 15 1.2.3. FUNCTION SPACES. CLASSES OF
DOMAINS 17 1.2.4. IMBEDDING THEOREMS 35 1.2.5. SPACES WITH NEGATIVE
NORMS 42 1.3. INTEGRAL OPERATORS 43 1.3.1. SINGULAR INTEGRALS 43 1.3.2.
SINGULAR INTEGRAL OPERATORS IN WEIGHTED SPACES .... 45 1.3.3.
GENERALIZED HARDY-LITTLEWOOD INEQUALITY 50 CHAPTER 2. BOUNDARY VALUE
PROBLEMS FOR THE STOKES SYSTEM 55 2.1. STATEMENT OF THE BOUNDARY VALUE
PROBLEMS AND THE GREEN FORMULAS 55 2.1.1. STATEMENT OF THE BOUNDARY
VALUE PROBLEMS 55 2.1.2. THE GREEN FORMULAS AND THE PROBLEMS FORMALLY
ADJOINT WITH RESPECT TO THEM 56 2.2. THE GREEN MATRICES ON THE
HALF-SPACE AND THE HALF-PLANE 60 2.2.1. GREEN MATRICES 60 2.2.2. THE
MAIN PROPERTIES OF THE GREEN MATRICES 64 2.3. WEIGHTED SPACES OF
FUNCTIONS ON E^ 66 2.3.1. WEIGHTED SOBOLEV SPACES 66 VII VLLL 2.3.2.
SPACES OF TRACES 69 2.3.3. SPACES WITH NEGATIVE NORMS 74 2.3.4. WEIGHTED
HOLDER SPACES 76 2.4. STRONG SOLVABILITY OF THE BOUNDARY VALUE PROBLEMS
IN THE HALF-SPACE 83 2.4.1. THE FIRST BOUNDARY VALUE PROBLEM IN WEIGHTED
SOBOLEV SPACES 83 2.4.2. SOLVABILITY OF THE SECOND BOUNDARY VALUE
PROBLEM . 91 2.4.3. SOLVABILITY OF THE BOUNDARY VALUE PROBLEMS IN
WEIGHTED HOLDER CLASSES 92 2.5. GENERALIZED SOLUTIONS OF BOUNDARY VALUE
PROBLEMS 101 2.5.1. AUXILIARY PROPOSITIONS 101 2.5.2. GENERALIZED
SOLUTIONS OF THE BOUNDARY VALUE PROBLEMS FOR THE STOKES SYSTEM 105
2.5.3. SOLVABILITY OF THE BOUNDARY VALUE PROBLEMS IN WEIGHTED HOLDER
SPACES 114 2.6. WEAK SOLUTIONS OF THE BOUNDARY VALUE PROBLEMS IN THE
HALF-SPACE 124 2.6.1. THE FIRST BOUNDARY VALUE PROBLEM 124 2.6.2. THE
SECOND BOUNDARY VALUE PROBLEM 127 2.7. PERTURBED BOUNDARY VALUE
PROBLEMS IN THE HALF-SPACE ... 132 2.7.1. THE FIRST BOUNDARY VALUE
PROBLEM 132 2.7.2. THE FIRST BOUNDARY VALUE PROBLEM IN WEIGHTED HOLDER
CLASSES 138 2.7.3. THE SECOND BOUNDARY VALUE PROBLEM 141 2.8. LOCAL
SOLUTIONS IN HALF-SPACE 148 2.8.1. THE FIRST BOUNDARY VALUE PROBLEM 148
2.8.2. THE SECOND BOUNDARY VALUE PROBLEM 157 2.9. LOCAL PROPERTIES OF
SOLUTIONS NEAR BOUNDARY 166 2.9.1. LOCAL ESTIMATES OF SOLUTIONS NEAR
BOUNDARY 166 2.9.2. THE CASE OF TWO INDEPENDENT VARIABLES 174 CHAPTER 3.
BOUNDARY VALUE PROBLEMS IN PLANE AND BIHEDRAL ANGLES 176 3.1. FUNCTION
SPACES 177 3.1.1. WEIGHTED SOBOLEV SPACES 177 3.1.2. WEIGHTED HOLDER
SPACES 179 CONTENTS IX 3.2. MODEL PROBLEMS IN PLANE ANGLE 182 3.2.1.
AUXILIARY PROBLEM IN ARC 183 3.2.2. FINDING OF THE MAXIMAL STRIP ON THE
COMPLEX PLANE WITHOUT SPECTRA OF THE BOUNDARY VALUE PROBLEMS ... 189
3.2.3. SOLVABILITY IN WEIGHTED HILBERT SPACES OF MODEL PROBLEMS IN PLANE
ANGLE 193 3.3. BOUNDARY VALUE PROBLEMS DEPENDING ON A PARAMETER 209
3.3.1. BOUNDARY VALUE PROBLEMS DEPENDING ON PARAMETER IN INTERVAL 209
3.3.2. AUXILIARY BOUNDARY VALUE PROBLEMS IN A PLANE ANGLE 218 3.3.3. THE
NOETHER PROPERTY OF BOUNDARY VALUE PROBLEMS AND COERCIVE ESTIMATES 225
3.3.4. UNIQUE SOLVABILITY OF THE BOUNDARY VALUE PROBLEMS IN A PLANE
ANGLE 238 3.4. SOLVABILITY IN WEIGHTED HILBERT SPACES OF THE BOUNDARY
VALUE PROBLEMS IN A BIHEDRAL ANGLE 242 3.4.1. SOLVABILITY OF THE
BOUNDARY VALUE PROBLEMS IN WEIGHTED SOBOLEV SPACES 243 3.4.2. THE
BOUNDARY VALUE PROBLEMS IN WEIGHTED HILBERT SPACES WITH NEGATIVE NORMS
245 3.4.3. LOCAL ESTIMATES 253 3.5. THE GREEN MATRICES OF THE BOUNDARY
VALUE PROBLEMS IN A BIHEDRAL ANGLE 262 3.5.1. EXISTENCE OF THE GREEN
MATRIX 262 3.5.2. THE MAIN PROPERTIES OF THE GREEN MATRIX AND POINTWISE
ESTIMATES OF ITS ELEMENTS 266 3.6. L S -ESTIMATES OF SOLUTIONS TO THE
BOUNDARY VALUE PROBLEMS IN BIHEDRAL ANGLE 277 3.6.1. ESTIMATES OF
SOLUTIONS IN WEIGHTED SOBOLEV SPACES 277 3.6.2. UNIQUE SOLVABILITY OF
THE BOUNDARY VALUE PROBLEMSIN WEIGHTED SOBOLEV SPACES 282 3.7. ESTIMATES
OF SOLUTIONS TO THE BOUNDARY VALUE PROBLEMS IN A VARIATIONAL FORM BY
WEIGHTED 5 -NORMS 283 3.7.1. A PRIORI ESTIMATES OF SOLUTIONS 283
3.7.2. UNIQUE SOLVABILITY OF THE BOUNDARY VALUE PROBLEMS IN GENERALIZED
SENSE 291 X 3.8. SOLVABILITY OF THE BOUNDARY VALUE PROBLEMS IN WEIGHTED
HOLDER SPACES 292 3.8.1. ESTIMATES OF SOLUTIONS OF THE BOUNDARY VALUE
PROBLEMS IN WEIGHTED HOLDER SPACES 292 3.8.2. SOLVABILITY OF THE PROBLEM
(3.4.1), (3.4.2) IN WEIGHTED HOLDER SPACES 294 CHAPTER 4. THE FIRST
BOUNDARY VALUE PROBLEM IN A GIVEN DOMAIN 295 4.1. CLASSES C L A 295
4.1.1. HOLDER CLASSES 295 4.1.2. DIFFERENTIAL OPERATORS 300 4.2. CLASSES
N L A 302 4.2.1. WEIGHTED HOLDER CLASSES 302 4.2.2. CONTINUOUS
DIFFERENTIAL OPERATORS IN WEIGHTED HOLDER SPACES 306 4.2.3.
DIFFEOMORPHISMS PRESERVING SPACES 308 4.3. SPACES ^(Q,M) 309 4.3.1.
WEIGHTED SOBOLEV SPACES 309 4.3.2. DIFFERENTIAL OPERATORS 310 4.4. THE
FIRST BOUNDARY VALUE PROBLEM IN A BOUNDED ANGULAR DOMAIN 311 4.4.1.
SIMPLE CONNECTED DOMAIN 311 4.4.2. FUNCTION SPACES 317 4.4.3.
GENERALIZED SOLUTION 318 4.4.4. THE BOUNDARY VALUE PROBLEM IN WEIGHTED
SOBOLEV SPACES 321 4.5. THE FIRST BOUNDARY VALUE PROBLEM FOR THE
NAVIER-STOKES SYSTEM IN DOMAINS WITH NONCOMPACT BOUNDARIES 333 4.5.1.
SPACES OF SOLENOIDAL VECTOR-FUNCTIONS ON DOMAINS WHOSE EXITS TO
INFINITY CONTAIN A CONE 333 4.5.2. SPACES OF SOLENOIDAL VECTOR-FUNCTIONS
ON DOMAINS WITH NONCOMPACT BOUNDARIES 343 4.5.3. THE FIRST BOUNDARY
VALUE PROBLEM FOR THE NAVIER-STOKES SYSTEM 356 CHAPTER 5. STEADY MOTION
OF A FLUID WITH A FREE SURFACE 363 5.1. STATEMENT OF THE PROBLEM 363
CONTENTS XI 5.2. THE EXTENSION THEOREM 365 5.2.1. NOTATION AND AUXILIARY
PROPOSITIONS 366 5.2.2. THE EXTENSION THEOREM 369 5.3. AUXILIARY LINEAR
PROBLEM IN A GIVEN BOUNDED DOMAIN .. . 375 5.3.1. PROPERTIES OF THE
DOMAIN AND DIFFEOMORPHISMS OF THE CLASS N L+3 - A N C L - X 375 5.3.2.
AUXILIARY PROPOSITIONS 379 5.3.3. THE NOETHER PROPERTY OF THE BOUNDARY
VALUE PROBLEM AND A PRIORI ESTIMATE 390 5.3.4. SOLVABILITY OF THE
BOUNDARY VALUE PROBLEM IN HILBERT SPACES 400 5.4. SOLVABILITY OF THE
BOUNDARY VALUE PROBLEM IN WEIGHTED HOLDER AND SOBOLEV SPACES 406 5.4.1.
SOLVABILITY IN NJ A (G) X IV 61|Q (G) 406 5.4.2. SOLVABILITY IN N^J^G) X
N LS + A (G) AND V 5 + 2+ ,(G) X 409 5.5. AUXILIARY NONLINEAR
PROBLEM 412 5.6. VARIATION OF THE SOLUTION TO THE AUXILIARY PROBLEM IN A
VARYING DOMAIN 414 5.7. SOLVABILITY OF THE FREE BOUNDARY PROBLEM 423
5.8. THE TWO-DIMENSIONAL FREE BOUNDARY PROBLEM 434 5.9. THE CASE OF
COMPLETE WETTING 442 5.9.1. STATEMENT OF THE PROBLEM 442 5.9.2.
AUXILIARY PROPOSITIONS 444 5.9.3. GENERALIZED SOLUTION 455 5.9.4.
WEIGHTED HOLDER SPACES 466 5.9.5. A CLASSICAL SOLUTION OF AN AUXILIARY
LINEARIZED PROBLEM 481 5.9.6. A NONLINEAR AUXILIARY PROBLEM 498 5.9.7.
VARIATION OF THE SOLUTION TO THE AUXILIARY PROBLEM IN A VARYING DOMAIN
500 5.9.8. SOLVABILITY OF THE FREE BOUNDARY PROBLEM 507 APPENDIX 1. THE
GREEN MATRICES ON THE HALF-SPACE AND HALF-PLANE 518 1. THE GREEN
MATRICES ON THE HALF-SPACE 518 2. THE GREEN MATRICES ON THE HALF-PLANE
528 XLL APPENDIX 2. WEIGHTED SCHAUDER ESTIMATES OF SOLUTIONS TO ELLIPTIC
BOUNDARY VALUE PROBLEMS 530 1. FUNCTION SPACES 530 2. ESTIMATES OF THE
SOLUTION OF THE BOUNDARY VALUE PROBLEM IN THE HALF-SPACE 532 3.
REPRESENTATION OF THE SOLUTION TO THE BOUNDARY VALUE PROBLEM IN THE
HALF-SPACE 539 4. THE BOUNDARY VALUE PROBLEM IN A BOUNDED DOMAIN 542
REFERENCES 550 SUBJECT INDEX 559 NOTATION INDEX 563
|
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| genre_facet | Konferenzschrift |
| id | DE-604.BV010423323 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-09T17:52:16Z |
| institution | BVB |
| isbn | 0792335090 |
| language | English Russian |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-006944243 |
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| owner_facet | DE-12 DE-703 DE-706 DE-634 DE-11 |
| physical | XV, 566 S. |
| publishDate | 1995 |
| publishDateSearch | 1995 |
| publishDateSort | 1995 |
| publisher | Kluwer |
| record_format | marc |
| series | Mathematics and its applications |
| series2 | Mathematics and its applications |
| spelling | Stupelis, Liudas Verfasser aut Navier-Stokes equations in irregular domains by L. Stupelis Dordrecht u.a. Kluwer 1995 XV, 566 S. txt rdacontent n rdamedia nc rdacarrier Mathematics and its applications 326 Navier-Stokes, équations ram Navier-Stokes equations Freies Randwertproblem (DE-588)4155303-2 gnd rswk-swf Navier-Stokes-Gleichung (DE-588)4041456-5 gnd rswk-swf (DE-588)1071861417 Konferenzschrift gnd-content Navier-Stokes-Gleichung (DE-588)4041456-5 s Freies Randwertproblem (DE-588)4155303-2 s DE-604 Mathematics and its applications 326 (DE-604)BV008163334 326 GBV Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=006944243&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Stupelis, Liudas Navier-Stokes equations in irregular domains Mathematics and its applications Navier-Stokes, équations ram Navier-Stokes equations Freies Randwertproblem (DE-588)4155303-2 gnd Navier-Stokes-Gleichung (DE-588)4041456-5 gnd |
| subject_GND | (DE-588)4155303-2 (DE-588)4041456-5 (DE-588)1071861417 |
| title | Navier-Stokes equations in irregular domains |
| title_auth | Navier-Stokes equations in irregular domains |
| title_exact_search | Navier-Stokes equations in irregular domains |
| title_full | Navier-Stokes equations in irregular domains by L. Stupelis |
| title_fullStr | Navier-Stokes equations in irregular domains by L. Stupelis |
| title_full_unstemmed | Navier-Stokes equations in irregular domains by L. Stupelis |
| title_short | Navier-Stokes equations in irregular domains |
| title_sort | navier stokes equations in irregular domains |
| topic | Navier-Stokes, équations ram Navier-Stokes equations Freies Randwertproblem (DE-588)4155303-2 gnd Navier-Stokes-Gleichung (DE-588)4041456-5 gnd |
| topic_facet | Navier-Stokes, équations Navier-Stokes equations Freies Randwertproblem Navier-Stokes-Gleichung Konferenzschrift |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=006944243&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV008163334 |
| work_keys_str_mv | AT stupelisliudas navierstokesequationsinirregulardomains |