Uncertainty estimates and L_2 bounds for the Kuramoto-Sivashinsky equation

Details Uncertainty estimates and L_2 bounds for the Kuramoto-Sivashinsky equation Uncertainty estimates and L_2 bounds for the Kuramoto-Sivashinsky equation

2005-08-24

arxiv.org/abs/math/0508481v2

Mathematics

Analysis of PDEs

17 pages, 1 figure; typos corrected, references added; figure modified

Scientific paper

10.1088/0951-7715/19/9/002

We consider the Kuramoto-Sivashinsky (KS) equation in one spatial dimension with periodic boundary conditions. We apply a Lyapunov function argument similar to the one first introduced by Nicolaenko, Scheurer, and Temam, and later improved by Collet, Eckmann, Epstein and Stubbe, and Goodman, to prove that ||u||_2 < C L^1.5. This result is slightly weaker than that recently announced by Giacomelli and Otto, but applies in the presence of an additional linear destabilizing term. We further show that for a large class of Lyapunov functions \phi the exponent 1.5 is the best possible from this line of argument. Further, this result together with a result of Molinet gives an improved estimate for L_2 boundedness of the Kuramoto-Sivashinsky equation in thin rectangular domains in two spatial dimensions.

Affiliated with

Also associated with

No associations

Rating

Uncertainty estimates and L_2 bounds for the Kuramoto-Sivashinsky equation does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Uncertainty estimates and L_2 bounds for the Kuramoto-Sivashinsky equation, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Uncertainty estimates and L_2 bounds for the Kuramoto-Sivashinsky equation will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-263197