Well-posedness for the Cahn-Hilliard-Navier-Stokes Equations Perturbed by Gradient-Type Noise, in Two Dimensions
In this work, we study the problem of existence and uniqueness of solutions of the stochastic Cahn-Hilliard-Navier-Stokes system with gradient-type noise. We show that such kind of noise is related to the problem of modelling turbulence. We apply a rescaling argument to transform the stochastic syst...
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| creator | Munteanu, Ionuţ |
| description | In this work, we study the problem of existence and uniqueness of solutions of the stochastic Cahn-Hilliard-Navier-Stokes system with gradient-type noise. We show that such kind of noise is related to the problem of modelling turbulence. We apply a rescaling argument to transform the stochastic system into a random deterministic one. We split the latter into two parts: the Navier-Stokes part and the Cahn-Hilliard part, respectively. The rescale operators possess good properties which allow to show that the rescaled Navier-Stokes equations have a unique solution, by appealing to
δ
-
monotone operators theory. While, well-posedness of the Cahn-Hilliard part is proved via a fixed point argument. Then, again a fixed point argument is used to prove global in time existence of a unique solution to the initial system. All the results are under the requirement that the initial data is in a certain small neighbourhood of the origin. |
| doi_str_mv | 10.1007/s00245-024-10121-w |
| format | Article |
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δ
-
monotone operators theory. While, well-posedness of the Cahn-Hilliard part is proved via a fixed point argument. Then, again a fixed point argument is used to prove global in time existence of a unique solution to the initial system. All the results are under the requirement that the initial data is in a certain small neighbourhood of the origin.</description><identifier>ISSN: 0095-4616</identifier><identifier>EISSN: 1432-0606</identifier><identifier>DOI: 10.1007/s00245-024-10121-w</identifier><language>eng</language><publisher>New York: Springer US</publisher><subject>Applied mathematics ; Calculus of Variations and Optimal Control; Optimization ; Control ; Fixed points (mathematics) ; Fluid flow ; Mathematical and Computational Physics ; Mathematical Methods in Physics ; Mathematics ; Mathematics and Statistics ; Navier-Stokes equations ; Numerical and Computational Physics ; Operators ; Optimization ; Phase transitions ; Rescaling ; Simulation ; Stochastic systems ; Systems Theory ; Theoretical ; Uniqueness ; Velocity ; Viscosity ; Well posed problems</subject><ispartof>Applied mathematics & optimization, 2024-04, Vol.89 (2), p.54, Article 54</ispartof><rights>The Author(s), under exclusive licence to Springer Science+Business Media, LLC, part of Springer Nature 2024. Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.</rights><lds50>peer_reviewed</lds50><woscitedreferencessubscribed>false</woscitedreferencessubscribed><cites>FETCH-LOGICAL-c270t-10f598420d6ab2b5af034acf792c08f476dd6b3e1dae9533f404a99f3e08ef943</cites><orcidid>0000-0002-0252-8517</orcidid></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktopdf>$$Uhttps://link.springer.com/content/pdf/10.1007/s00245-024-10121-w$$EPDF$$P50$$Gspringer$$H</linktopdf><linktohtml>$$Uhttps://link.springer.com/10.1007/s00245-024-10121-w$$EHTML$$P50$$Gspringer$$H</linktohtml><link.rule.ids>314,780,784,27924,27925,41488,42557,51319</link.rule.ids></links><search><creatorcontrib>Munteanu, Ionuţ</creatorcontrib><title>Well-posedness for the Cahn-Hilliard-Navier-Stokes Equations Perturbed by Gradient-Type Noise, in Two Dimensions</title><title>Applied mathematics & optimization</title><addtitle>Appl Math Optim</addtitle><description>In this work, we study the problem of existence and uniqueness of solutions of the stochastic Cahn-Hilliard-Navier-Stokes system with gradient-type noise. We show that such kind of noise is related to the problem of modelling turbulence. We apply a rescaling argument to transform the stochastic system into a random deterministic one. We split the latter into two parts: the Navier-Stokes part and the Cahn-Hilliard part, respectively. The rescale operators possess good properties which allow to show that the rescaled Navier-Stokes equations have a unique solution, by appealing to
δ
-
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δ
-
monotone operators theory. While, well-posedness of the Cahn-Hilliard part is proved via a fixed point argument. Then, again a fixed point argument is used to prove global in time existence of a unique solution to the initial system. All the results are under the requirement that the initial data is in a certain small neighbourhood of the origin.</abstract><cop>New York</cop><pub>Springer US</pub><doi>10.1007/s00245-024-10121-w</doi><orcidid>https://orcid.org/0000-0002-0252-8517</orcidid></addata></record> |
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| subjects | Applied mathematics Calculus of Variations and Optimal Control Optimization Control Fixed points (mathematics) Fluid flow Mathematical and Computational Physics Mathematical Methods in Physics Mathematics Mathematics and Statistics Navier-Stokes equations Numerical and Computational Physics Operators Optimization Phase transitions Rescaling Simulation Stochastic systems Systems Theory Theoretical Uniqueness Velocity Viscosity Well posed problems |
| title | Well-posedness for the Cahn-Hilliard-Navier-Stokes Equations Perturbed by Gradient-Type Noise, in Two Dimensions |
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