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We have decided to discontinue the publication of preprints on our preprint server as of 1 March 2024. The publication culture within mathematics has changed so much due to the rise of repositories such as ArXiV (www.arxiv.org) that we are encouraging all institute members to make their preprints available there. An institute's repository in its previous form is, therefore, unnecessary. The preprints published to date will remain available here, but we will not add any new preprints here.

MiS Preprint
24/2015

New bounds for the inhomogenous Burgers and the Kuramoto-Sivashinsky equations

Michael Goldman, Marc Josien and Felix Otto

Abstract

We give a substantially simplified proof of the near-optimal estimate on the Kuramoto-Sivashinsky equation from [14], at the same time slightly improving the result. The result in [14] relied on two ingredients: a regularity estimate for capillary Burgers and an a novel priori estimate for the inhomogeneous inviscid Burgers equation, which works out that inmany ways the conservative transport nonlinearity acts as a coercive term. It is the proof of the second ingredient that we substantially simplify by proving a modified Kármán-Howarth-Monin identity for solutions of the inhomogeneous inviscid Burgers equation. We showthat this provides a new interpretation of the results obtained in [7].

Received:
Mar 25, 2015
Published:
Mar 25, 2015

Related publications

inJournal
2015 Repository Open Access
Michael Goldman, Marc Josien and Felix Otto

New bounds for the inhomogenous Burgers and the Kuramoto-Sivashinsky equations

In: Communications in partial differential equations, 40 (2015) 12, pp. 2237-2265