分数阶Navier-Stokes方程解的爆破准则
On the blow-up criterion for solutions of 3D fractional Navier-Stokes equations
徐郜婷 1孙小春1
作者信息
- 1. 西北师范大学数学与统计学院,甘肃兰州 730070
- 折叠
摘要
首先证明了分数阶三维不可压缩Navier-Stokes方程在齐次Sobolev空间(H˙) s中解的存在性,其中α>1/2,max{5/2-2α,0}<s<3/2.其次在最大时间Tν∗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,研究了解在(H˙) s空间中的爆破性和L2范数的衰减性,以及解关于Fourier变换的L1范数的下界估计.这是对Benameur J等人(2010)对经典Navier-Stokes方程所得出结论的推广.
Abstract
The existence of solutions to the fractional 3D incompressible Navier-Stokes equations in homogeneous Sobolev spaces (H˙) s is firstly proved in this paper,where α>1/2,max{5/2-2α,0}<s<3/2.Secondly,when the maximum time Tν∗ is finite,the blow-up in (H˙) s spaces and the decay in L2 norm of the solution and the lower bounds estimate of the solution with respect to L1 norm of Fourier transform are studied,via using the property of Fourier transform,interpolation results and product law in the homogeneous Sobolev spaces.Finally,it's a generalization of the results obtained by Benameur J,et al(2010)on the classical Navier-Stokes equations.
关键词
分数阶Navier-Stokes方程/存在性/衰减性/爆破准则Key words
fractional Navier-Stokes equation/existence/decay/blow-up criterion引用本文复制引用
出版年
2024
NETL
NSTL
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