Global special regular solutions to the Navier-Stokes equations in axially symmetric domains under boundary slip conditions:
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| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Warszawa
Inst. of Mathematics, Polish Acad. of Sciences
2005
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| Series: | Dissertationes mathematicae
432 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | 138, II S. |
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Record in the Search Index
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| adam_text |
Titel: Global special regular solutions to the Navier-Stokes equations in axially symmetric domains under b
Autor: Zaja̜czkowski, Wojciech M
Jahr: 2005
CONTENTS
Introduction.
1. Formulation of main results.
1.1. Reformulation of the main problem.
1.2. Main results.
1.3. Outline of proof of the main results.
2. Notation and auxiliary results.
2.1. Spaces and notation.
2.2. Imbedding and trace theorems.
2.3. Estimates for some elliptic and parabolic problems.
2.4. Differential operators in cylindrical coordinates.
3. Boundary conditions for velocity and vorticity.
3.1. Boundary conditions for velocity in cylindrical coordinates.
3.2. Boundary conditions for vorticity.
3.3. Energy type estimates for velocity and its angular derivative h.
3.4. Reformulation of the problem for the azimuthal component of the vorticity x
4. Estimates for vorticity and azimuthal derivatives of velocity.
4.1. Energy estimate for x.
4.2. Estimate of h in weighted Sobolev spaces.
4.3. Estimates of vorticity in weighted Sobolev spaces.
5. Estimates for the azimuthal coordinate of velocity.
6. Local existence: boundedness of the approximating sequence.
6.1. Formulation of the method of successive approximations.
6.2. Estimate of the first step.
6.3. Estimate of the general step.
7. Local existence: convergence of the approximating sequence.
7.1. Problems for differences.
7.2. Estimates of differences.
7.3. Local existence.
8. Global existence.
8.1. Idea of the proof.
8.2. Decay estimates.
8.3. Proof of global existence.
9. Historical overview.
9.1. Problems with slip boundary conditions.
9.2. Local existence and uniqueness of strong solutions.
9.3. Conditional regularity.
9.4. Singular and regular points.
9.5. Blow-up problems.*.
9.6. Continuation of the local strong solution.
9.7. Global special regular solutions.
9.8. Decay of solutions.
References.
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[3] |
| adam_txt |
Titel: Global special regular solutions to the Navier-Stokes equations in axially symmetric domains under b
Autor: Zaja̜czkowski, Wojciech M
Jahr: 2005
CONTENTS
Introduction.
1. Formulation of main results.
1.1. Reformulation of the main problem.
1.2. Main results.
1.3. Outline of proof of the main results.
2. Notation and auxiliary results.
2.1. Spaces and notation.
2.2. Imbedding and trace theorems.
2.3. Estimates for some elliptic and parabolic problems.
2.4. Differential operators in cylindrical coordinates.
3. Boundary conditions for velocity and vorticity.
3.1. Boundary conditions for velocity in cylindrical coordinates.
3.2. Boundary conditions for vorticity.
3.3. Energy type estimates for velocity and its angular derivative h.
3.4. Reformulation of the problem for the azimuthal component of the vorticity x
4. Estimates for vorticity and azimuthal derivatives of velocity.
4.1. Energy estimate for x.
4.2. Estimate of h in weighted Sobolev spaces.
4.3. Estimates of vorticity in weighted Sobolev spaces.
5. Estimates for the azimuthal coordinate of velocity.
6. Local existence: boundedness of the approximating sequence.
6.1. Formulation of the method of successive approximations.
6.2. Estimate of the first step.
6.3. Estimate of the general step.
7. Local existence: convergence of the approximating sequence.
7.1. Problems for differences.
7.2. Estimates of differences.
7.3. Local existence.
8. Global existence.
8.1. Idea of the proof.
8.2. Decay estimates.
8.3. Proof of global existence.
9. Historical overview.
9.1. Problems with slip boundary conditions.
9.2. Local existence and uniqueness of strong solutions.
9.3. Conditional regularity.
9.4. Singular and regular points.
9.5. Blow-up problems.*.
9.6. Continuation of the local strong solution.
9.7. Global special regular solutions.
9.8. Decay of solutions.
References.
5
7
8
10
13
16
16
17
25
27
28
28
29
31
34
35
35
39
40
54
64
64
65
71
78
78
79
104
105
105
105
112
115
115
116
120
126
128
128
129
132
133
[3] |
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| index_date | 2024-07-02T13:40:19Z |
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| language | English |
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| physical | 138, II S. |
| publishDate | 2005 |
| publishDateSearch | 2005 |
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| publisher | Inst. of Mathematics, Polish Acad. of Sciences |
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| series | Dissertationes mathematicae |
| series2 | Dissertationes mathematicae |
| spelling | Zajączkowski, Wojciech M. Verfasser (DE-588)1089338880 aut Global special regular solutions to the Navier-Stokes equations in axially symmetric domains under boundary slip conditions Wojciech M. Zajączkowski Warszawa Inst. of Mathematics, Polish Acad. of Sciences 2005 138, II S. txt rdacontent n rdamedia nc rdacarrier Dissertationes mathematicae 432 Boundary value problems Numerical solutions Differential equations Numerical solutions Navier-Stokes equations Numerical solutions Navier-Stokes-Gleichung (DE-588)4041456-5 gnd rswk-swf Navier-Stokes-Gleichung (DE-588)4041456-5 s DE-604 Dissertationes mathematicae 432 (DE-604)BV000003039 432 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=014576351&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Zajączkowski, Wojciech M. Global special regular solutions to the Navier-Stokes equations in axially symmetric domains under boundary slip conditions Dissertationes mathematicae Boundary value problems Numerical solutions Differential equations Numerical solutions Navier-Stokes equations Numerical solutions Navier-Stokes-Gleichung (DE-588)4041456-5 gnd |
| subject_GND | (DE-588)4041456-5 |
| title | Global special regular solutions to the Navier-Stokes equations in axially symmetric domains under boundary slip conditions |
| title_auth | Global special regular solutions to the Navier-Stokes equations in axially symmetric domains under boundary slip conditions |
| title_exact_search | Global special regular solutions to the Navier-Stokes equations in axially symmetric domains under boundary slip conditions |
| title_exact_search_txtP | Global special regular solutions to the Navier-Stokes equations in axially symmetric domains under boundary slip conditions |
| title_full | Global special regular solutions to the Navier-Stokes equations in axially symmetric domains under boundary slip conditions Wojciech M. Zajączkowski |
| title_fullStr | Global special regular solutions to the Navier-Stokes equations in axially symmetric domains under boundary slip conditions Wojciech M. Zajączkowski |
| title_full_unstemmed | Global special regular solutions to the Navier-Stokes equations in axially symmetric domains under boundary slip conditions Wojciech M. Zajączkowski |
| title_short | Global special regular solutions to the Navier-Stokes equations in axially symmetric domains under boundary slip conditions |
| title_sort | global special regular solutions to the navier stokes equations in axially symmetric domains under boundary slip conditions |
| topic | Boundary value problems Numerical solutions Differential equations Numerical solutions Navier-Stokes equations Numerical solutions Navier-Stokes-Gleichung (DE-588)4041456-5 gnd |
| topic_facet | Boundary value problems Numerical solutions Differential equations Numerical solutions Navier-Stokes equations Numerical solutions Navier-Stokes-Gleichung |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=014576351&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV000003039 |
| work_keys_str_mv | AT zajaczkowskiwojciechm globalspecialregularsolutionstothenavierstokesequationsinaxiallysymmetricdomainsunderboundaryslipconditions |