ISSN:
1432-0916
Source:
Springer Online Journal Archives 1860-2000
Topics:
Mathematics
,
Physics
Notes:
Abstract New bounds are given for the L2-norm of the solution of the Kuramoto-Sivashinsky equation $$\partial _t U(x,t) = - (\partial _x^2 + \partial _x^4 )U(x,t) - U(x,t)\partial _x U(x,t)$$ , for initial data which are periodic with periodL. There is no requirement on the antisymmetry of the initial data. The result is $$\mathop {\lim \sup }\limits_{t \to \infty } \left\| {U( \cdot ,t)} \right\|_2 \leqslant const. L^{8/5} $$ .
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1007/BF02097064
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