CRM: Centro De Giorgi
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Equazioni alle Derivate Parziali nella Dinamica dei Fluidi

Zero Viscosity Limit for Analytic Solutions of the Primitive Equations

speaker: Maria Carmela Lombardo (Università di Palermo)

abstract: In this talk we shall address the vanishing viscosity limit and analyze the structure of the boundary layer for solutions of the Primitive Equations with the non-slip boundary condition on the bottom of the domain. Under the hypothesis of spatial analyticity of the initial datum, we shall prove that the solutions of the Primitive Equations converge, in the zero viscosity limit, to the solutions of the Hydrostatic equations. We construct the solution of the Primitive Equation through a matched asymptotic expansion involving the solution of the Hydrostatic equation and Boundary Layer correctors as the first order term, and an error that we show to be $O(\sqrt{\nu})$.

Mon 5 Feb, 11:45 - 12:20, Aula Dini
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