Navier–Stokes flow in the exterior of a moving obstacle with a Lipschitz boundary
arxiv(2024)
摘要
Consider the three-dimensional Navier–Stokes flow past a moving rigid body
𝒪⊂ℝ^3 with prescribed translational and angular
velocities, where 𝒪 stands for a bounded Lipschitz domain. We prove
that the solution to the linearized problem is governed by a C_0-semigroup on
solenoidal L^q-vector spaces with the L^q-L^r estimates provided that
|1/q-1/2|<1/6+ε with some ε>0, where r ≥ q may be
taken arbitrary large. As an application, we prove the existence and uniqueness
of global mild solutions to the Navier–Stokes problem if the translational and
angular velocities as well as the initial are sufficiently small.
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