数学与统计学院知识库

本文研究了具有 \alpha\in(0,1) 阶时间分数导数的 Navier-Stokes 时滞微分包含. 首先, 我们利用分数阶豫解算子理论和一些非紧性测度的技巧, 证明了当初值在 C([-h,0];D(A_r^\varepsilon)) 时, 适度解的局部存在性, 全局存在性, 衰减性以及正则性. 然后我们给出了一个例子，来说明我们结果的可适用性。

In this paper, we study a Navier-Stokes delay differential inclusion with time fractional derivative of order \alpha\in(0,1). We first prove the local and global existence, decay and regularity properties of mild solutions when the initial data belongs to C([-h,0];D(A_r^\varepsilon)). The fractional resolvent operator theory and some techniques of measure of noncompactness are successfully applied to obtain the results.  An example is also given to illustrate the feasibility of our abstract results.