Details

Autor(en) / Beteiligte

• WINKLER, MICHAEL

Titel

How far do chemotaxis-driven forces influence regularity in the Navier-Stokes system?

Ist Teil von

• Transactions of the American Mathematical Society, 2017-05, Vol.369 (5), p.3067-3125

Ort / Verlag

American Mathematical Society

Erscheinungsjahr

2017

Link zum Volltext

Quelle

EZB Free E-Journals

Beschreibungen/Notizen

• is considered under boundary conditions of homogeneous Neumann type for n and c, and Dirichlet type for u, in a bounded convex domain \Omega \subset \mathbb{R}^3 with smooth boundary, where \Phi \in W^{1,\infty }(\Omega ) and \chi and f are sufficiently smooth given functions generalizing the prototypes \chi \equiv const. and f(s)=s for s\ge 0. hold as t\to \infty , uniformly with respect to x\in \Omega . This resembles a classical result on the three-dimensional Navier-Stokes system, asserting eventual smoothness of arbitrary weak solutions thereof which additionally fulfill the associated natural energy inequality. In consequence, our results inter alia indicate that under the considered boundary conditions, the possibly destabilizing action of chemotactic cross-diffusion in ( \star ) does not substantially affect the regularity properties of the fluid flow at least on large time scales.]]>