Effective Estimates of the Higher Sobolev Norms for the Kuramoto-sivashinsky Equation
نویسندگان
چکیده
We consider the Kuramoto-Sivashinsky (KS) equation in finite domains of the form [−L, L]. Our main result provides effective new estimates for higher Sobolev norms of the solutions in terms of powers of L for the onedimentional differentiated KS. We illustrate our method on a simpler model, namely the regularized Burger’s equation. The underlying idea in this result is that a priori control of the L2 norm is enough in order to conclude higher order regularity and in fact, it allows one to get good estimates on the high-frequency tails of the solution.
منابع مشابه
The Kuramoto-sivashinsky Equation in R and R: Effective Estimates of the High-frequency Tails and Higher Sobolev Norms
We consider the Kuramoto-Sivashinsky (KS) equation in finite domains of the form [−L,L]d. Our main result provides refined Gevrey estimates for the solutions of the one dimensional differentiated KS, which in turn imply effective new estimates for higher Sobolev norms of the solutions in terms of powers of L. We illustrate our method on a simpler model, namely the regularized Burger’s equation....
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