Large time behavior of a generalized Oseen evolution operator, with applications to the Navier-Stokes flow past a rotating obstacle

Toshiaki Hishida

Large time behavior of a generalized Oseen evolution operator, with applications to the Navier-Stokes flow past a rotating obstacle

Analysis of PDEs 2019-08-13 v2

Authors: Toshiaki Hishida

Abstract

Consider the motion of a viscous incompressible fluid in a 3D exterior domain when a rigid body moves with prescribed time-dependent translational and angular velocities. For the linearized non-autonomous system, $L^q$ - $L^r$ smoothing action near the initial time as well as generation of the evolution operator was shown by Hansel and Rhandi (J. Reine Angew. Math. 2014) under reasonable conditions. In this paper we develop the $L^q$ - $L^r$ decay estimates of the evolution operator and then apply them to the Navier-Stokes initial value problem.

Keywords

Oseen evolution operator Navier-Stokes flow rotating obstacle L^q-L^r decay estimates non-autonomous system

Cite

@article{arxiv.1706.03344,
  title  = {Large time behavior of a generalized Oseen evolution operator, with applications to the Navier-Stokes flow past a rotating obstacle},
  author = {Toshiaki Hishida},
  journal= {arXiv preprint arXiv:1706.03344},
  year   = {2019}
}

Comments

38 pages, Corrected typos, to appear in Math. Ann

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