Solutions to the Navier--Stokes Equations with Mixed Boundary Conditions in Two-Dimensional Bounded Domains

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F68407700%3A21110%2F16%3A00225681" target="_blank" >RIV/68407700:21110/16:00225681 - isvavai.cz</a>
Result on the web
<a href="http://dx.doi.org/10.1002/mana.201400046" target="_blank" >http://dx.doi.org/10.1002/mana.201400046</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1002/mana.201400046" target="_blank" >10.1002/mana.201400046</a>

Result language
angličtina
Original language name
Solutions to the Navier--Stokes Equations with Mixed Boundary Conditions in Two-Dimensional Bounded Domains
Original language description
In this paper we consider the system of the non--steady Navier--Stokes equations with mixed boundary conditions. We study the existence and uniqueness of a solution of this system. We define Banach spaces $X$ and $Y$, respectively, to be the space of ``possible'' solutions of this problem and the space of its data. We define the operator $on:Xto Y$ and formulate our problem in terms of operator equations. Let $bfuin X$ and $ogpu: Xto Y$ be the Frechet derivative of $on$ at $bfu$. We prove that $ogpu$ is one-to-one and onto $Y$. Consequently, suppose that the system is solvable with some given data (the initial velocity and the right hand side). Then there exists a unique solution of this system for data which are small perturbations of the previous ones. Next result proved in the Appendix of this paper is $W^{2,2}$- regularity of solutions of steady Stokes system with mixed boundary condition for sufficiently smooth data.
Czech name
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Czech description
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Type
J<sub>x</sub> - Unclassified - Peer-reviewed scientific article (Jimp, Jsc and Jost)
CEP classification
BA - General mathematics
OECD FORD branch
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Project
Result was created during the realization of more than one project. More information in the Projects tab.
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Publication year
2016
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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