Artículos de revistas
Vanishing Viscosity For Non-homogeneous Asymmetric Fluids In R3
Registro en:
Journal Of Mathematical Analysis And Applications. , v. 332, n. 2, p. 833 - 845, 2007.
0022247X
10.1016/j.jmaa.2006.10.066
2-s2.0-34247340187
Autor
Braz e Silva P.
Fernandez-Cara E.
Rojas-Medar M.A.
Institución
Resumen
We consider a non-homogeneous, viscous, incompressible asymmetric fluid in R3. We prove that there exists a small time interval where the fluid variables converge uniformly as the viscosities tend to zero. In the limit, we find a non-homogeneous, non-viscous, incompressible asymmetric fluid governed by an Euler-like system. © 2006 Elsevier Inc. All rights reserved. 332 2 833 845 Antonzev, S.N., Kazhikov, A.V., Monakhov, V.N., (1990) Boundary Value Problems in Mechanics of Nonhomogeneous Fluids, , North-Holland, Amsterdam Boldrini, J.L., Rojas-Medar, M., Fernández-Cara, E., Semi-Galerkin approximation and strong solutions to the equations of the nonhomogeneous asymmetric fluids (2003) J. Math. Pures Appl., 82 (11), pp. 1499-1525 Caflisch, R.E., Sammartino, M., Existence and singularities for the Prandtl boundary layer equations (2000) Z. Angew. Math. Mech., 80, pp. 11-12. , 733-744 Condiff, D.W., Dahler, J.S., Fluid mechanics aspects of antisymmetric stress (1964) Phys. Fluids, 7 (6), pp. 842-854 Itoh, S., On the vanishing viscosity in the Cauchy problem for the equations of a nonhomogeneos incompressible fluids (1994) Glasg. Math. J., 36, pp. 123-129 Itoh, S., Tani, A., Solvability of nonstationary problems for nonhomogeneous inompressible fluids and the convergence with vanishing viscosity (1999) Tokyo J. Math., 22, pp. 17-42 Kazhikov, A.V., Solvability of the initial and boundary-value problem for the equations of motion of an inhomogeneous viscous incompressible fluid (1974) Dokl. Akad. Nauk, 216, pp. 1008-1010. , English translation: Kazhikov, A.V., Solvability of the initial and boundary-value problem for the equations of motion of an inhomogeneous viscous incompressible fluid (1974) Soviet Phys. Dokl., pp. 331-332 Kim, J.U., Weak solutions of an initial boundary value problem for an incompressible viscous fluids (1987) SIAM J. Math. Anal., 18, pp. 890-896 Ladyzhenskaya, O.A., (1969) The Mathematical Theory of Viscous Incompressible Flow. second revised ed., , Gordon and Breach, New York Ladyzhenskaya, O.A., Solonnikov, V.A., Unique solvability of an initial and boundary value problem for viscous incompressible fluids (1975) Zap. Nauchn. Sem. Leningrad Otdel Math. Inst. Steklov, 52, pp. 52-109. , English translation: Ladyzhenskaya, O.A., Solonnikov, V.A., Unique solvability of an initial and boundary value problem for viscous incompressible fluids (1978) J. Soviet Math., 9, pp. 697-749 Lions, J.L., On some questions in boundary value problems of mathematical physics (1978) Contemporary Developments in Continuum Mechanics and Partial Differential Equations, , de la Penha G.M., and Medeiros L.A. (Eds), North-Holland, Amsterdam Lions, J.L., On some problems connected with Navier-Stokes equations (1978) Nonlinear Evolution Equations, , Crandall M.C. (Ed), Academic Press, New York Lions, P.L., (1996) Mathematical Topics in Fluid Dynamics, vol. 1: Incompressible Models, , Clarendon Press, Oxford University Press, New York Lukaszewicz, G., On nonstationary flows of incompressible asymmetric fluids (1990) Math. Methods Appl. Sci. 19, 13 (3), pp. 219-232 Lukaszewicz, G., (1998) Micropolar Fluids: Theory and Applications, , Birkhäuser, Berlin Salvi, R., The equations of viscous incompressible nonhomogeneous fluid: On the existence and regularity (1991) J. Aust. Math. Soc. Ser. B Appl. Math., 33, pp. 94-110. , (Part 1) Simon, J., Nonhomogeneous viscous incompressible fluids: Existence of velocity, density, and pressure (1990) SIAM J. Math. Anal., 21, pp. 1073-1117 Temam, R., (1979) Navier-Stokes Equations, Theory and Numerical Analysis, , North-Holland, Amsterdam