Existence and Uniqueness of Solutions of a Quasilinear Approximation of the 3D Navier–Stokes System
- 47 Downloads
For the quasilinear approximation of the 3D Navier–Stokes system proposed earlier by the authors in , some conditions of solution regularity are considered and the theorem on existence and uniqueness of the Cauchy problem for some class of initial data is proved.
KeywordsInitial Data Cauchy Problem System Theory Stokes System Solution Regularity
Unable to display preview. Download preview PDF.
- 1.Dinaburg, E.I. and Sinai, Ya.G., A Quasi-Linear Approximation of Three-Dimensional Navier–Stokes System, Moscow Math. J., 2001, vol. 1, no. 3, pp. 381–388.Google Scholar
- 2.Nelineinye sistemy gidrodinamicheskogo tipa (Nonlinear Systems of Hydrodinamical Type), Obukhov, A.M., Ed., Moscow: Nauka, 1974.Google Scholar
- 3.E, W. and Sinai, Ya.G., Recent Results on Mathematical and Statistical Hydrodinamics, Usp. Mat. Nauk, 2000, vol. 55, no. 4, pp. 25–59 [Russian Math. Surveys (Engl. Transl.), 2000, vol. 55, no. 4, pp. 635–666].Google Scholar
- 4.Dinaburg, E.I., New Finite-Dimensional Approximations of the 3D Navier–Stokes System, Dokl. Ross. Akad. Nauk, 2002, vol. 383, pp. 151–155 [Dokl. Math. (Engl. Transl.), 2002, vol. 65, no. 2, pp. 175–179].Google Scholar