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.

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