We show that every L-periodic, mean-zero solution u of the Kuramoto-Sivashinsky equation is on average o(L) for L>>1, in the sense that for any T > 0 the space average of |u(t)| is bounded by LT for any t > T and any L sufficiently large. For this we argue that on large spatial scales, the solution behaves like an entropy solution of the inviscid Burgers equation. The analysis of this nonstandard perturbation of the Burgers equation is based on a “div-curl” argument.
New bounds for the Kuramoto-Sivashinsky equation / Giacomelli, Lorenzo; F., Otto. - In: COMMUNICATIONS ON PURE AND APPLIED MATHEMATICS. - ISSN 0010-3640. - STAMPA. - 58:(2005), pp. 297-318. [10.1002/cpa.20031]
New bounds for the Kuramoto-Sivashinsky equation
GIACOMELLI, Lorenzo;
2005
Abstract
We show that every L-periodic, mean-zero solution u of the Kuramoto-Sivashinsky equation is on average o(L) for L>>1, in the sense that for any T > 0 the space average of |u(t)| is bounded by LT for any t > T and any L sufficiently large. For this we argue that on large spatial scales, the solution behaves like an entropy solution of the inviscid Burgers equation. The analysis of this nonstandard perturbation of the Burgers equation is based on a “div-curl” argument.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
