Strong solutions of the Navier–Stokes equations based on the maximal Lorentz regularity theorem in Besov spaces
Strong solutions of the Navier–Stokes equations based on the maximal Lorentz regularity theorem in Besov spaces
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DOI：
10.1016/j.jfa.2018.06.006
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发表时间：
2019-02
影响因子：
1.7
通讯作者：
H. Kozono;Senjo Shimizu
中科院分区：
文献类型：
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作者：
H. Kozono;Senjo Shimizu
在尺度不变的具有正负微分阶的齐次Besov空间中，证明了具有任意初值和外力的Navier-Stokes方程局部强解的存在唯一性定理.如果初始数据和外力都很小，那么局部解可以在时间上扩展到全局。我们的解决方案也属于Serrin类在通常的Lebesgue空间。该方法基于齐次Besov空间中Stokes方程的极大Lorentz正则性定理。作为应用，我们还可以处理球上的Dirac测度和单层势等奇异数据。
We show existence and uniqueness theorem of local strong solutions to the Navier–Stokes equations with arbitrary initial data and external forces in the homogeneous Besov space with both negative and positive differential orders which is an invariant space under the change of scaling. If the initial data and external forces are small, then the local solutions can be extended globally in time. Our solutions also belong to the Serrin class in the usual Lebesgue space. The method is based on the maximal Lorentz regularity theorem of the Stokes equations in the homogeneous Besov spaces. As an application, we may handle such singular data as the Dirac measure and the single layer potential supported on the sphere.