Space-time asymptotics of the two dimensional Navier-Stokes flow in the whole plane

作者：Okabe Takahiro^*

来源：Journal of Differential Equations, 2018, 264(2): 728-754.

DOI：10.1016/j.jde.2017.09.025

• Time decay
• Asymptotic expansion
• Large time behavior

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 L-1(R-2) boolean AND L-sigma(2) (R-2). Moreover, we characterize the necessary and sufficient condition for the rapid energy decay parallel to u(t)parallel to(2) = o(t(-1)) as t -> infinity 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 H-1 (R-2) for t > 0, we consider the asymptotic expansions in terms of Hardy-norm. Finally we consider the rapid time decay parallel to u(t)parallel to(2) = o(t-(3/2)) as t -> infinity with cyclic symmetry introduced by Brandolese [2].

• 出版日期2018-1-15