Artículos de revistas
Vanishing Viscosity Limit For Incompressible Flow Inside A Rotating Circle
Registro en:
Physica D: Nonlinear Phenomena. , v. 237, n. 10-12, p. 1324 - 1333, 2008.
1672789
10.1016/j.physd.2008.03.009
2-s2.0-44649120782
Autor
Lopes Filho M.C.
Mazzucato A.L.
Nussenzveig Lopes H.J.
Institución
Resumen
In this article we consider circularly symmetric incompressible viscous flow in a disk. The boundary condition is no-slip with respect to a prescribed time-dependent rotation of the boundary about the center of the disk. We prove that, if the prescribed angular velocity of the boundary has finite total variation, then the Navier-Stokes solutions converge strongly in L2 to the corresponding stationary solution of the Euler equations when viscosity vanishes. Our approach is based on a semigroup treatment of the symmetry-reduced scalar equation. © 2008 Elsevier B.V. All rights reserved. 237 10-12 1324 1333 K. Asano, Zero viscosity limit of incompressible Navier-Stokes equations I, II, unpublished preprints, 1988Bona, J., Wu, J., The zero-viscosity limit of the 2D Navier-Stokes equations (2002) Stud. Appl. Math., 109 (4), pp. 265-278 Clopeau, T., Mikelic, A., Robert, R., On the vanishing viscosity limit for the 2D incompressible Navier-Stokes equations with friction-type boundary conditions (1998) Nonlinearity, 11, pp. 1625-1636 Folland, G., (1999) Pure and Applied Mathematics (New York), , A Wiley-Interscience Publication, New York Grenier, E., Masmoudi, N., Ekman layers of rotating fluids, the case of well prepared initial data (1997) Comm. Partial Differential Equations, 22 (5-6), pp. 953-975 Henry, D., (1981) Lecture Notes in Mathematics, 840. , Springer-Verlag, Berlin, New York Iftimie, D., Planas, G., Inviscid limits for the Navier-Stokes equations with Navier friction boundary conditions (2006) Nonlinearity, 19, pp. 899-918 Kato, T., Remarks on zero viscosity limit for nonstationary Navier-Stokes flows with boundary (1984) Seminar on Nonlinear PDE, , Chern S.S. (Ed), MSRI, Berkeley Kelliher, J., On Kato's conditions for vanishing viscosity (2007) Indiana Univ. Math. J., 56 (4), pp. 1711-1721 J. Kelliher, On the vanishing viscosity limit in a disk, preprint, 2007Lax, P.D., Functional analysis (2002) Pure and Applied Mathematics (New York), , Wiley-Interscience, New York M. Lopes Filho, A. Mazzucato, H. Nussenzveig Lopes, M. Taylor, Vanishing viscosity limits and boundary layers for circularly symmetric 2D flows, Bull. Braz. Math. Soc. (in press)Lopes Filho, M., Nussenzveig Lopes, H., Planas, G., On the inviscid limit for two-dimensional incompressible flow with Navier friction condition (2005) SIAM J. Appl. Math., 36 (4), pp. 1130-1141 Lopes Filho, M., Nussenzveig Lopes, H., Zheng, Y., Convergence of the vanishing viscosity approximation for superpositions of confined eddies (1999) Comm. Math. Phys., 201 (2), pp. 291-304 Masmoudi, N., The Euler limit of the Navier-Stokes equations and rotating fluids with boundary (1998) Arch. Ration. Mech. Anal., 142 (4), pp. 375-394 Matsui, S., Example of zero viscosity limit for two-dimensional nonstationary Navier-Stokes flows with boundary (1994) Japan J. Indust. Appl. Math., 11 (1), pp. 155-170 Pazy, A., (1983) Applied Mathematical Sciences, 44. , Springer-Verlag, New York Reed, M., Simon, B., Methods of modern mathematical physics. II (1975) Fourier Analysis, Self-Adjointness, , Academic Press, New York, London Sammartino, M., Caflisch, R., Zero viscosity limit for analytic solutions of the Navier-Stokes equation on a half-space I, existence for Euler and Prandtl equations (1998) Comm. Math. Phys., 192 (2), pp. 433-461 Sammartino, M., Caflisch, R., Zero viscosity limit for analytic solutions of the Navier-Stokes equation on a half-space II, construction of the Navier-Stokes solution (1998) Comm. Math. Phys., 192 (2), pp. 463-491 Schlichting, H., Gersten, K., (2000) Boundary Layer Theory. 8th edition, , Springer Verlag, Berlin Temam, R., Wang, X., On the behavior of the solutions of the Navier-Stokes equations at vanishing viscosity (1998) Annali della Scuola Norm. Sup. Pisa Serie IV XXV, pp. 807-828. , (Vol. dedicated to the memory of E. De Giorgi) Temam, R., Wang, X., Boundary layer associated with the incompressible Navier-Stokes equations: The non-characteristic boundary case (2002) J. Differential Equations, 179, pp. 647-686 Wang, X., A Kato type theorem on zero viscosity limit of Navier-Stokes flows (2001) Indiana Univ. Math. J., 50 (1), pp. 223-241