论文标题
Wiener Amalgam空间中的Stokes和Navier-Stokes流的轻度解决方案和时空积分界
Mild solutions and spacetime integral bounds for Stokes and Navier-Stokes flows in Wiener amalgam spaces
论文作者
论文摘要
我们首先证明了在amalgam空间中的Stokes Flow的衰减估算和时空积分界限$ e^r_q $，这些$ e^r_q $将经典的lebesgue空间连接到均匀的本地$ r $ rub-integrable函数的空间。使用这些估计值，我们在满足相应时空积分边界的汞合金空间中构建了navier-Stokes方程的温和解。 $ e^3_q $，$ 1 \ le q \ le 3 $中的小数据构建了时间全球解决方案。我们的结果为加藤经典的强大解决方案以及由Maekawa和Terasawa建造的统一的本地空间提供了新的界限。作为应用程序，我们获得了针对弱解决方案对扰动的Navier-Stokes方程的稳定性的结果，在该方程中，漂移速度求解Navier-Stokes方程，并且在本地$ L^3 $类中具有少量数据。为了扩展较早的结果，我们还以$ e^2_q $，$ 1 \ le q <2 $构建全球本地能源弱解决方案。
We first prove decay estimates and spacetime integral bounds for Stokes flows in amalgam spaces $E^r_q$ which connect the classical Lebesgue spaces to the spaces of uniformly locally $r$-integrable functions. Using these estimates, we construct mild solutions of the Navier-Stokes equations in the amalgam spaces satisfying the corresponding spacetime integral bounds. Time-global solutions are constructed for small data in $E^3_q$, $1\le q \le 3$. Our results provide new bounds for the strong solutions classically constructed by Kato and the more recent solutions in uniformly local spaces constructed by Maekawa and Terasawa. As an application we obtain a result on the stability of suitability for weak solutions to the perturbed Navier-Stokes equation where the drift velocity solves the Navier-Stokes equations and has small data in a local $L^3$ class. Extending an earlier result, we also construct global-in-time local energy weak solutions in $E^2_q$, $1\le q <2$.
