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

作　　者：徐郜婷 孙小春 XU Gao-ting;SUN Xiao-chun(College of Mathematics and Statistics,Northwest Normal University,Lanzhou 730070,China)

机构地区：[1]西北师范大学数学与统计学院,甘肃兰州730070

出　　处：《高校应用数学学报（A辑）》2024年第2期175-181,共7页Applied Mathematics A Journal of Chinese Universities(Ser.A)

基　　金：国家自然科学基金(11601434)。

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T_(v)^(*)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L^(2)范数的衰减性,以及解关于Fourier变换的L^(1)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.The existence of solutions to the fractional 3D incompressible Navier-Stokes equations in homogeneous Sobolev spacesH^(s) is¯rstly proved in this paper,whereα>1/2;max{5/2-2α;0}<s<3/2.Secondly,when the maximum time T_(v)^(*)is finite,the blow-up in H^(s) spaces and the decay in L^(2) norm of the solution and the lower bounds estimate of the solution with respect to L^(1) 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 

分 类 号：O174.2[理学—数学]