论文标题
时间周期性粘性流的空间衰减经过一个身体
Spatial decay of the vorticity field of time-periodic viscous flow past a body
论文作者
论文摘要
我们研究了涡度场的渐近空间行为，即$ω（x，t）$，与弱解决方案中的$ \ mathscr b $相关的时间，$ \ mathscr b $，在满足锯齿蛋白样条件的弱解决方案中。我们表明，在唤醒区域之外，$ \ MATHCAL R $，$ω$以指数级的速度（及时）均匀地衰减。 Moreover, denoting by $\barω$ its time-average over a period and by $ω_P:=ω-\barω$ its purely periodic component, we prove that inside $\mathcal R$, $\barω$ has the same algebraic decay as that known for the associated steady-state problem, whereas $ω_P$ decays even faster, uniformly in time.这特别意味着与$ \ Mathscr b $，$ω（x，t）$“足够远”的行为就像相应的稳态问题的涡度字段一样。
We study the asymptotic spatial behavior of the vorticity field, $ω(x,t)$, associated to a time-periodic Navier-Stokes flow past a body, $\mathscr B$, in the class of weak solutions satisfying a Serrin-like condition. We show that, outside the wake region, $\mathcal R$, $ω$ decays pointwise at an exponential rate, uniformly in time. Moreover, denoting by $\barω$ its time-average over a period and by $ω_P:=ω-\barω$ its purely periodic component, we prove that inside $\mathcal R$, $\barω$ has the same algebraic decay as that known for the associated steady-state problem, whereas $ω_P$ decays even faster, uniformly in time. This implies, in particular, that "sufficiently far" from $\mathscr B$, $ω(x,t)$ behaves like the vorticity field of the corresponding steady-state problem.
