Estimates for solutions of the nonstationary Stokes problem in anisotropic sobolev spaces with mixed norm

被引:0
作者
Maremonti P.
Solonnikov V.A.
机构
关键词
Sobolev Space; Wide Class; Stokes Problem; Stokes Operator; Mixed Norm;
D O I
10.1007/BF02355828
中图分类号
学科分类号
摘要
A new method is given to establish Lq,r-estimates for solutions of the nonstationary Stokes problem. The method is based on estimates for heat potentials in these spaces, and it is not connected with investigation of the resolvent for the Stokes operator. It is expected that the method is applicable to a wide class of parabolic initial boundary-value problems. ©1997 Plenum Publishing Corporation.
引用
收藏
页码:3859 / 3877
页数:18
相关论文
共 11 条
[1]  
Solonnikov V.A., Estimates of solutions for the nonstationary linearized system of Navier-Stokes equations, Trudy Mat. Inst. Akad. Nauk SSSR, 70, pp. 213-317, (1964)
[2]  
Solonnikov V.A., Estimates for solutions of the nonstationary Navier-Stokes equations, Zap. Nauchn. Semin. LOMI, 38, pp. 153-231, (1973)
[3]  
Yudovich V.I., Method of Linearization in Hydrodynamical Stability Theory, (1984)
[4]  
Giga Y., Sohr H., Abstract L<sub>p</sub>-estimates for the Cauchy problem with applications to the Navier-Stokes equations in exterior domains, J. Funct. Anal., 102, pp. 72-94, (1991)
[5]  
Solonnikov V.A., A-priori estimates for second order equations of parabolic type, Trudy Mat. Inst. Akad. Nauk SSSR, 70, pp. 133-212, (1964)
[6]  
Ladyzhenskaya O.A., Solonnikov V.A., Uraltseva N.N., Linear and Quasilinear Equations of Parabolic Type, (1967)
[7]  
Besov O.V., Il'In V.P., Nikol'Skii S.N., Integral Representations of Functions and Embedding Theorems, (1975)
[8]  
Golovkin K.K., On equivalent normalizations of fractional spaces, Trudy Mat. Inst. Akad. Nauk SSSR, 66, pp. 364-383, (1962)
[9]  
Bugrov Ja. S., Embedding theorems for classes of functions with a mixed norm, Mat. Sb., 92, pp. 611-621, (1973)
[10]  
Iwashita H., L<sub>q</sub> - L<sub>r</sub> estimates for solutions of the nonstationary Stokes equations in an exterior domain and the Navier-Stokes initial value problems in L<sub>q</sub> spaces, Math. Ann., 295, pp. 265-288, (1989)