TY - JOUR

T1 - On some dissipative fully discrete nonlinear Galerkin schemes for the Kuramoto-Sivashinsky equation

AU - Foias, C.

AU - Jolly, M. S.

AU - Kevrekidis, I. G.

AU - Titi, E. S.

N1 - Funding Information:
The work of C.F. was supported in part by NSF Grants DMS-8802596 and DMS-9007802, that of M.S.J. also by NSF grant DMS-9007802, that of I.G.IC in part by NSF Grant ECS-9023362 and the David and Lucile Packard Foundation, and that of E.S.T. in part by the AFOSR, NSF Grant DMS-8915672, and by the Graduate Council Fund of the University of California, Irvine.

PY - 1994/3/7

Y1 - 1994/3/7

N2 - We show that two fully discrete nonlinear Galerkin schemes based on explicit approximate inertial manifolds preserve the dissipativity of the Kuramoto-Sivashinsky equation (KSE). The radius of the absorbing ball is shown to be uniform in both the time step and number of modes, so that the result holds in the PDE limit. While the schemes are specifically designed to deal with the difficulty of the linear instability in the KSE, simpler schemes can be derived following this approach for other dissipative nonlinear evolutionary equations, such as the 2D Navier-Stokes equations.

AB - We show that two fully discrete nonlinear Galerkin schemes based on explicit approximate inertial manifolds preserve the dissipativity of the Kuramoto-Sivashinsky equation (KSE). The radius of the absorbing ball is shown to be uniform in both the time step and number of modes, so that the result holds in the PDE limit. While the schemes are specifically designed to deal with the difficulty of the linear instability in the KSE, simpler schemes can be derived following this approach for other dissipative nonlinear evolutionary equations, such as the 2D Navier-Stokes equations.

UR - http://www.scopus.com/inward/record.url?scp=38149144940&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=38149144940&partnerID=8YFLogxK

U2 - 10.1016/0375-9601(94)90926-1

DO - 10.1016/0375-9601(94)90926-1

M3 - Article

AN - SCOPUS:38149144940

SN - 0375-9601

VL - 186

SP - 87

EP - 96

JO - Physics Letters, Section A: General, Atomic and Solid State Physics

JF - Physics Letters, Section A: General, Atomic and Solid State Physics

IS - 1-2

ER -