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dc.contributor.authorHaspot, Boris
dc.date.accessioned2011-10-28T13:48:43Z
dc.date.available2011-10-28T13:48:43Z
dc.date.issued2011
dc.identifier.urihttps://basepub.dauphine.fr/handle/123456789/7355
dc.language.isoenen
dc.subjectcapillarity termen
dc.subjectviscosityen
dc.subjectshallow-water equationsen
dc.subject.ddc515en
dc.titleExistence of global strong solutions for the shallow-water equations with large initial dataen
dc.typeDocument de travail / Working paper
dc.description.abstractenThis work is devoted to the study of a viscous shallow-water system with friction and capillarity term. We prove in this paper the existence of global strong solutions for this system with some choice of large initial data when $N\geq 2$ in critical spaces for the scaling of the equations. More precisely, we introduce as in \cite{Hprepa} a new unknown,\textit{a effective velocity} $v=u+\mu\n\ln h$ ($u$ is the classical velocity and $h$ the depth variation of the fluid) with $\mu$ the viscosity coefficient which simplifies the system and allow us to cancel out the coupling between the velocity $u$ and the depth variation $h$. We obtain then the existence of global strong solution if $m_{0}=h_{0}v_{0}$ is small in $B^{\N-1}_{2,1}$ and $(h_{0}-1)$ large in $B^{\N}_{2,1}$. In particular it implies that the classical momentum $m_{0}^{'}=h_{0} u_{0}$ can be large in $B^{\N-1}_{2,1}$, but small when we project $m_{0}^{'}$ on the divergence field. These solutions are in some sense \textit{purely compressible}. We would like to point out that the friction term term has a fundamental role in our work inasmuch as coupling with the pressure term it creates a damping effect on the effective velocity.en
dc.publisher.nameUniversité Paris-Dauphineen
dc.publisher.cityParisen
dc.identifier.citationpages15en
dc.identifier.urlsitehttp://hal.archives-ouvertes.fr/hal-00636462/fr/en
dc.description.sponsorshipprivateouien
dc.subject.ddclabelAnalyseen


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