分数阶Navier-Stokes方程在齐次Sobolev空间中解的爆破准则  

On the Blow-Up Criterion for Solutions of 3D Fractional Navier-Stokes Equations in Homogeneous Sobolev Spaces

作　　者：徐郜婷 孙小春[1] 吴育联 

机构地区：[1]西北师范大学,甘肃 兰州

出　　处：《应用数学进展》2023年第1期231-239,共9页Advances in Applied Mathematics

摘　　要：本文在最大时间Tv*有限时,利用Fourier变换的性质,齐次Sobolev空间中的插值结果以及乘积定理,研究了分数阶三维不可压缩Navier-Stokes方程在齐次Sobolev空间Hs中解的爆破性和L2范数的衰减性,以及解关于H2-a范数、范数和范数的有界性,是对Benameur J的经典Navier-Stokes方程结论的推广。In this paper, when the maximum time Tv* is finite, the blow-up of the solutions to the fractional 3D incompressible Navier-Stokes equations in Hs spaces and the decay in L2 norm and the boundedness of the solution with respect to H2-a norm, norm and norm are stud-ied, via using the property of Fourier transform, interpolation results and product law in the homo-geneous Sobolev spaces. It’s a generalization of the classical Navier-Stokes equations conclusion of Benameur J.

关 键 词：分数阶Navier-Stokes方程 衰减性 爆破准则 

分 类 号：O17[理学—数学]