Cauchy problem for viscous shallow water equations with a term of capillarity
Haspot, Boris (2010), Cauchy problem for viscous shallow water equations with a term of capillarity, Mathematical Models and Methods in Applied Sciences, 20, 7, p. 1049. http://dx.doi.org/10.1142/S0218202510004532
TypeArticle accepté pour publication ou publié
Journal nameMathematical Models and Methods in Applied Sciences
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Abstract (EN)In this article , we consider the compressible Navier-Stokes equation with density dependent viscosity coefficients and a term of capillarity introduced formally by Van der Waals in . This model includes at the same time the barotropic Navier-Stokes equations with variable viscosity coefficients, shallow-water system and the model introduced by Rohde in . We first study the well-posedness of the model in critical regularity spaces with respect to the scaling of the associated equations. In a functional setting as close as possible to the physical energy spaces, we prove global existence of solutions close to a stable equilibrium, and local in time existence of solutions with general initial data. Uniqueness is also obtained.
Subjects / Keywordsshallow-water system; viscosity; Navier–Stokes equations; Cauchy problem
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