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Equazioni alle Derivate Parziali nella Dinamica dei Fluidi

Navier-Stokes past a rigid body: attainability of steady solutions as limits of unsteady weak solutions, starting and landing cases

speaker: Paolo Maremonti (Università degli Studi della Campania "L. Vanvitelli")

abstract: Consider the Navier–Stokes flow in 3-dimensional exterior domains, where a rigid body is translating with pre-scribed translational velocity −\(h(t)u_\infty\) with constant vector \(u_\infty ∈ R^3\{0\}\). Finn raised the question whether his steady solutions are attainable as limits for \(t\to\infty\) of unsteady solutions starting from motionless state when \(h(t) = 1\) after some finite time and \(h(0) = 0\) (starting problem). This was affirmatively solved by Galdi et al. for small \(u_\infty\). We study some generalized situation in which unsteady solutions start from large motions being in \(L^3_w\). We then conclude that the steady solutions for small \(u_\infty\) are still attainable as limits of evolution of those fluid motions which are found as a sort of weak solutions. The opposite situation, in which \(h(t) = 0\) after some finite time and \(h(0) = 1\) (landing problem), is also discussed. In this latter case, the rest state is attainable no matter how large \(u_\infty\) is.

Mon 5 Feb, 16:10 - 16:45, Aula Dini
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