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
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。
Abstract: 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.
文章引用：徐郜婷, 孙小春, 吴育联. 分数阶Navier-Stokes方程在齐次Sobolev空间中解的爆破准则[J]. 应用数学进展, 2023, 12(1): 231-239. https://doi.org/10.12677/AAM.2023.121026

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