The Cauchy problem for the homogeneous time-dependent Oseen system in ℝ 3: spatial decay of the velocity

Title:

The Cauchy problem for the homogeneous time-dependent Oseen system in ℝ 3: spatial decay of the velocity

Creator:

Deuring, Paul

Identifier:

https://cdk.lib.cas.cz/client/handle/uuid:dfa49ba9-e175-4ce5-a29d-7983087d29a9
uuid:dfa49ba9-e175-4ce5-a29d-7983087d29a9
doi:10.21136/MB.2013.143439

Subject:

Cauchy problem, time-dependent Oseen system, spatial decay, and wake

Type:

model:article and TEXT

Format:

bez média and svazek

Description:

We consider the homogeneous time-dependent Oseen system in the whole space R 3 . The initial data is assumed to behave as O(|x| −1−ε ), and its gradient as O(|x| −3/2−ε ), when |x| tends to infinity, where ε is a fixed positive number. Then we show that the velocity u decays according to the equation |u(x, t)| = O(|x| −1 ), and its spatial gradient ∇xu decreases with the rate |x| −3/2 , for |x| tending to infinity, uniformly with respect to the time variable t. Since these decay rates are optimal even in the stationary case, they should also be the best possible in the evolutionary case considered in this article. We also treat the case ε = 0. Then the preceding decay rates of u remain valid, but they are no longer uniform with respect to t.

Language:

English

Rights:

http://creativecommons.org/publicdomain/mark/1.0/
policy:public

Coverage:

299-324

Source:

Mathematica bohemica | 2013 Volume:138 | Number:3

Harvested from:

CDK

Metadata only:

false