论文标题
在关键的规则空间中
Global unique solutions for the inhomogeneous Navier-Stokes equation with only bounded density, in critical regularity spaces
论文作者
论文摘要
在这里，我们旨在证明在初始密度不连续并且初始速度具有至关重要的规律性的情况下，在不均匀不可压缩的Navier-Stokes系统中，解决方案的全球存在和独特性。假设初始密度接近正常数，那么每当初始速度属于某种关键的均匀贝贝空间（在三维情况下，在较小的情况下），我们就会在二维情况下获得全局存在和唯一性。接下来，我们仍然处于关键功能框架中，我们建立了一个唯一性语句，在密度较大的情况下，可能会带有真空。有趣的是，我们的结果暗示着P. Zhang构建的藤田 - 喀托型解决方案是独一无二的。我们的工作依赖于插值结果，时间加权估计值和最大规律性估计值（相对于时间变量）的最大规律性估计值（相对于时间变量）。
We here aim at proving the global existence and uniqueness of solutions to the inhomogeneous incompressible Navier-Stokes system in the case where the initial density is discontinuous and the initial velocity has critical regularity. Assuming that the initial density is close to a positive constant, we obtain global existence and uniqueness in the two-dimensional case whenever the initial velocity belongs to some critical homogeneous Besov space (and in small in the three-dimensional case). Next, still in a critical functional framework, we establish a uniqueness statement that is valid in the case of large variations of density with, possibly, vacuum. Interestingly, our result implies that the Fujita-Kato type solutions constructed by P. Zhang in are unique. Our work relies on interpolation results, time weighted estimates and maximal regularity estimates in Lorentz spaces (with respect to the time variable) for the evolutionary Stokes system.
