Time-dependent incompressible viscous flows around a rigid body: estimates of spatial decay independent of boundary conditions - Archive ouverte HAL Access content directly
Preprints, Working Papers, ... Year : 2021

Time-dependent incompressible viscous flows around a rigid body: estimates of spatial decay independent of boundary conditions

Abstract

We consider the incompressible time-dependent Navier-Stokes system with Oseen term, in a 3D exterior domain, with the option of adding to the system another term arising in the study of stability of stationary incompressible Navier-Stokes flows. We do not impose any boundary conditions. The solutions we consider are supposed to possess properties of L^2-strong solutions: The velocity u is an L^∞-function in time and L^κ-integrable in space for some κ ∈ [1, 3) and some κ ∈ (3, ∞), the spatial gradient ∇_x u is L 2-integrable in space and in time, and the nonlinearity (u · ∇_x)u is L^2-integrable in time and L^3/2-integrable in space. We show that if the right-hand side of the equation and the initial data decay pointwise in space sufficiently fast, then u and ∇_x u also decay pointwise in space, with rates which are higher than those exhibited in previous articles.
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Dates and versions

hal-02508815 , version 1 (16-03-2020)
hal-02508815 , version 2 (02-09-2020)
hal-02508815 , version 3 (14-03-2021)

Identifiers

  • HAL Id : hal-02508815 , version 3

Cite

Paul Deuring. Time-dependent incompressible viscous flows around a rigid body: estimates of spatial decay independent of boundary conditions. 2021. ⟨hal-02508815v3⟩
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