Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
8899045 | Journal of Differential Equations | 2018 | 27 Pages |
Abstract
We consider the space-time behavior of the two dimensional Navier-Stokes flow. Introducing some qualitative structure of initial data, we succeed to derive the first order asymptotic expansion of the Navier-Stokes flow without moment condition on initial data in L1(R2)â©LÏ2(R2). Moreover, we characterize the necessary and sufficient condition for the rapid energy decay âu(t)â2=o(tâ1) as tââ motivated by Miyakawa-Schonbek [21]. By weighted estimated in Hardy spaces, we discuss the possibility of the second order asymptotic expansion of the Navier-Stokes flow assuming the first order moment condition on initial data. Moreover, observing that the Navier-Stokes flow u(t) lies in the Hardy space H1(R2) for t>0, we consider the asymptotic expansions in terms of Hardy-norm. Finally we consider the rapid time decay âu(t)â2=o(tâ32) as tââ with cyclic symmetry introduced by Brandolese [2].
Related Topics
Physical Sciences and Engineering
Mathematics
Analysis
Authors
Takahiro Okabe,