The solvability of stationary boundary problem for model of the granular medium |
A. A. Illarionov, A. Yu. Chebotarev |
2004, issue 2, P. 178–183 |
Abstract |
The solvability of the boundary problem for equations describing the stationary moving of incompressible medium with inner degrees of freedom is proved. |
Keywords: Navier-Stokes equation, model of the granular medium, weak solution |
Download the article (PDF-file) |
References |
[1] V. D. Lelyux, E. N. Nenashev, “K teorii dvizheniya sypuchej sredy v nepodvizhnoj gazovoj faze”, Primenenie analiticheskix i chislennyx metodov v mexanike zhidkix i sypuchix sred, Uch. zap. Gor'kov. un-ta. Ser. Mexanika, 156, Gor'kij, 1972, 4–20. [2] S. N. Antoncev, V. D. Lelyux, “O razreshimosti nachal'no-kraevoj zadachi v odnoj modeli dinamiki sredy s vnutrennimi stepenyami svobody”, Dinamika sploshnoj sredy, 1972, № 12, 26–51. [3] S. N. Antoncev, A. V. Kazhixov, V. N. Monaxov, Kraevye zadachi mexaniki neodnorodnyx zhidkostej, Nauka, Novosibirsk, 1983, 319 s. [4] N. N. Frolov, “O razreshimosti kraevoj zadachi dvizheniya neodnorodnoj zhidkosti”, Matem. zametki, 53:6 (1993), 130–140. [5] N. N. Frolov, “Kraevaya zadacha, opisyvayushhaya dvizhenie neodnorodnoj zhidkosti”, Sib. mat. zhurn., 37:2 (1996), 433–451. [6] A. Yu. Chebotarev, “Stacionarnye variacionnye neravenstva v modeli neodnorodnoj zhidkosti”, Sib. mat. zhurn., 38:5 (1997), 1185–1193. [7] V. Girault, P. Raviart, Finite element methods for Navier – Stokes equations, Springer-Verlag, New York, 1986. [8] D. Gilbarg, M. Trudinger, E'llipticheskie differencial'nye uravneniya s chastnymi proizvodnymi vtorogo poryadka, Nauka, M., 1989, 464 s. [9] O. A. Ladyzhenskaya, Matematicheskie voprosy dinamiki vyazkoj neszhimaemoj zhidkosti, Nauka, M., 1970, 288 s. |