dc.contributor.author Haspot, Boris dc.date.accessioned 2011-10-28T13:48:43Z dc.date.available 2011-10-28T13:48:43Z dc.date.issued 2011 dc.identifier.uri https://basepub.dauphine.fr/handle/123456789/7355 dc.language.iso en en dc.subject capillarity term en dc.subject viscosity en dc.subject shallow-water equations en dc.subject.ddc 515 en dc.title Existence of global strong solutions for the shallow-water equations with large initial data en dc.type Document de travail / Working paper dc.description.abstracten This 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.name Université Paris-Dauphine en dc.publisher.city Paris en dc.identifier.citationpages 15 en dc.identifier.urlsite http://hal.archives-ouvertes.fr/hal-00636462/fr/ en dc.description.sponsorshipprivate oui en dc.subject.ddclabel Analyse en
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