Stochastically Forced Compressible Fluid Flows /:
This book contains a first systematic study of compressible fluid flows subject to stochastic forcing. The bulk is the existence of dissipative martingale solutions to the stochastic compressible Navier-Stokes equations. These solutions are weak in the probabilistic sense as well as in the analytica...
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| Hauptverfasser: | , , |
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| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Berlin ; Boston :
De Gruyter,
[2018]
|
| Schriftenreihe: | De Gruyter series in applied and numerical mathematics ;
v. 3. |
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Zusammenfassung: | This book contains a first systematic study of compressible fluid flows subject to stochastic forcing. The bulk is the existence of dissipative martingale solutions to the stochastic compressible Navier-Stokes equations. These solutions are weak in the probabilistic sense as well as in the analytical sense. Moreover, the evolution of the energy can be controlled in terms of the initial energy. We analyze the behavior of solutions in short-time (where unique smooth solutions exists) as well as in the long term (existence of stationary solutions). Finally, we investigate the asymptotics with respect to several parameters of the model based on the energy inequality. ContentsPart I: Preliminary results Elements of functional analysis Elements of stochastic analysis Part II: Existence theory Modeling fluid motion subject to random effects Global existence Local well-posedness Relative energy inequality and weak-strong uniqueness Part III: Applications Stationary solutions Singular limits. |
| Beschreibung: | 1 online resource (342 pages). |
| ISBN: | 9783110492552 3110492555 9783110492569 3110492563 |
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| 505 | 0 | 0 | |t Frontmatter -- |t Acknowledgements -- |t Notation -- |t Contents -- |t Part I: Preliminary results -- |t 1. Elements of functional analysis -- |t 2. Elements of stochastic analysis -- |t Part II: Existence theory -- |t 3. Modeling fluid motion subject to random effects -- |t 4. Global existence -- |t 5. Local well-posedness -- |t 6. Relative energy inequality and weak-strong uniqueness -- |t Part III: Applications -- |t 7. Stationary solutions -- |t 8. Singular limits -- |t A. Appendix -- |t B. Bibliographical remarks -- |t Index. |
| 520 | |a This book contains a first systematic study of compressible fluid flows subject to stochastic forcing. The bulk is the existence of dissipative martingale solutions to the stochastic compressible Navier-Stokes equations. These solutions are weak in the probabilistic sense as well as in the analytical sense. Moreover, the evolution of the energy can be controlled in terms of the initial energy. We analyze the behavior of solutions in short-time (where unique smooth solutions exists) as well as in the long term (existence of stationary solutions). Finally, we investigate the asymptotics with respect to several parameters of the model based on the energy inequality. ContentsPart I: Preliminary results Elements of functional analysis Elements of stochastic analysis Part II: Existence theory Modeling fluid motion subject to random effects Global existence Local well-posedness Relative energy inequality and weak-strong uniqueness Part III: Applications Stationary solutions Singular limits. | ||
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| author | Breit, Dominic Feireisl, Eduard Hofmanová, Martina |
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| author_facet | Breit, Dominic Feireisl, Eduard Hofmanová, Martina |
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| contents | Frontmatter -- Acknowledgements -- Notation -- Contents -- Part I: Preliminary results -- 1. Elements of functional analysis -- 2. Elements of stochastic analysis -- Part II: Existence theory -- 3. Modeling fluid motion subject to random effects -- 4. Global existence -- 5. Local well-posedness -- 6. Relative energy inequality and weak-strong uniqueness -- Part III: Applications -- 7. Stationary solutions -- 8. Singular limits -- A. Appendix -- B. Bibliographical remarks -- Index. |
| ctrlnum | (OCoLC)1024055624 |
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| dewey-ones | 532 - Fluid mechanics |
| dewey-raw | 532/.05 |
| dewey-search | 532/.05 |
| dewey-sort | 3532 15 |
| dewey-tens | 530 - Physics |
| discipline | Physik |
| format | Electronic eBook |
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| indexdate | 2024-11-27T13:28:14Z |
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| spelling | Breit, Dominic, author. http://id.loc.gov/authorities/names/no2018057885 Stochastically Forced Compressible Fluid Flows / Dominic Breit, Eduard Feireisl, Martina Hofmanová. Berlin ; Boston : De Gruyter, [2018] ©2018 1 online resource (342 pages). text txt rdacontent computer c rdamedia online resource cr rdacarrier text file PDF rda De Gruyter series in applied and numerical mathematics ; volume 3 Frontmatter -- Acknowledgements -- Notation -- Contents -- Part I: Preliminary results -- 1. Elements of functional analysis -- 2. Elements of stochastic analysis -- Part II: Existence theory -- 3. Modeling fluid motion subject to random effects -- 4. Global existence -- 5. Local well-posedness -- 6. Relative energy inequality and weak-strong uniqueness -- Part III: Applications -- 7. Stationary solutions -- 8. Singular limits -- A. Appendix -- B. Bibliographical remarks -- Index. This book contains a first systematic study of compressible fluid flows subject to stochastic forcing. The bulk is the existence of dissipative martingale solutions to the stochastic compressible Navier-Stokes equations. These solutions are weak in the probabilistic sense as well as in the analytical sense. Moreover, the evolution of the energy can be controlled in terms of the initial energy. We analyze the behavior of solutions in short-time (where unique smooth solutions exists) as well as in the long term (existence of stationary solutions). Finally, we investigate the asymptotics with respect to several parameters of the model based on the energy inequality. ContentsPart I: Preliminary results Elements of functional analysis Elements of stochastic analysis Part II: Existence theory Modeling fluid motion subject to random effects Global existence Local well-posedness Relative energy inequality and weak-strong uniqueness Part III: Applications Stationary solutions Singular limits. In English. Online resource; title from PDF title page (publisher's Web site, viewed 19. Feb 2018). Fluid dynamics. http://id.loc.gov/authorities/subjects/sh85049376 Hydrodynamics https://id.nlm.nih.gov/mesh/D057446 Dynamique des fluides. TECHNOLOGY & ENGINEERING Hydraulics. bisacsh Fluid dynamics fast Feireisl, Eduard, author. http://id.loc.gov/authorities/names/nb2003112515 Hofmanová, Martina, author. http://id.loc.gov/authorities/names/no2018058041 Print version: Breit, Dominic. Stochastically forced compressible fluid flows. Berlin ; Boston : De Gruyter, [2018] 9783110490503 (OCoLC)1022944629 De Gruyter series in applied and numerical mathematics ; v. 3. http://id.loc.gov/authorities/names/no2017159685 FWS01 ZDB-4-EBA FWS_PDA_EBA https://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&AN=1691653 Volltext |
| spellingShingle | Breit, Dominic Feireisl, Eduard Hofmanová, Martina Stochastically Forced Compressible Fluid Flows / De Gruyter series in applied and numerical mathematics ; Frontmatter -- Acknowledgements -- Notation -- Contents -- Part I: Preliminary results -- 1. Elements of functional analysis -- 2. Elements of stochastic analysis -- Part II: Existence theory -- 3. Modeling fluid motion subject to random effects -- 4. Global existence -- 5. Local well-posedness -- 6. Relative energy inequality and weak-strong uniqueness -- Part III: Applications -- 7. Stationary solutions -- 8. Singular limits -- A. Appendix -- B. Bibliographical remarks -- Index. Fluid dynamics. http://id.loc.gov/authorities/subjects/sh85049376 Hydrodynamics https://id.nlm.nih.gov/mesh/D057446 Dynamique des fluides. TECHNOLOGY & ENGINEERING Hydraulics. bisacsh Fluid dynamics fast |
| subject_GND | http://id.loc.gov/authorities/subjects/sh85049376 https://id.nlm.nih.gov/mesh/D057446 |
| title | Stochastically Forced Compressible Fluid Flows / |
| title_alt | Frontmatter -- Acknowledgements -- Notation -- Contents -- Part I: Preliminary results -- 1. Elements of functional analysis -- 2. Elements of stochastic analysis -- Part II: Existence theory -- 3. Modeling fluid motion subject to random effects -- 4. Global existence -- 5. Local well-posedness -- 6. Relative energy inequality and weak-strong uniqueness -- Part III: Applications -- 7. Stationary solutions -- 8. Singular limits -- A. Appendix -- B. Bibliographical remarks -- Index. |
| title_auth | Stochastically Forced Compressible Fluid Flows / |
| title_exact_search | Stochastically Forced Compressible Fluid Flows / |
| title_full | Stochastically Forced Compressible Fluid Flows / Dominic Breit, Eduard Feireisl, Martina Hofmanová. |
| title_fullStr | Stochastically Forced Compressible Fluid Flows / Dominic Breit, Eduard Feireisl, Martina Hofmanová. |
| title_full_unstemmed | Stochastically Forced Compressible Fluid Flows / Dominic Breit, Eduard Feireisl, Martina Hofmanová. |
| title_short | Stochastically Forced Compressible Fluid Flows / |
| title_sort | stochastically forced compressible fluid flows |
| topic | Fluid dynamics. http://id.loc.gov/authorities/subjects/sh85049376 Hydrodynamics https://id.nlm.nih.gov/mesh/D057446 Dynamique des fluides. TECHNOLOGY & ENGINEERING Hydraulics. bisacsh Fluid dynamics fast |
| topic_facet | Fluid dynamics. Hydrodynamics Dynamique des fluides. TECHNOLOGY & ENGINEERING Hydraulics. Fluid dynamics |
| url | https://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&AN=1691653 |
| work_keys_str_mv | AT breitdominic stochasticallyforcedcompressiblefluidflows AT feireisleduard stochasticallyforcedcompressiblefluidflows AT hofmanovamartina stochasticallyforcedcompressiblefluidflows |