Estimates for solutions of a low-viscosity kick-forced generalized Burgers equation
Published online by Cambridge University Press: 18 March 2013
Abstract
We consider a non-homogeneous generalized Burgers equation
Here, ν is small and positive, f is strongly convex and satisfies a growth assumption, while ηω is a space-smooth random ‘kicked’ forcing term. For any solution u of this equation, we consider the quasi-stationary regime, corresponding to t ⩾ 2. After taking the ensemble average, we obtain upper estimates and time-averaged lower estimates for a class of Sobolev norms of u. These estimates are of the form Cν-β with the same values of β for bounds from above and from below. They depend on η and f, but do not depend on the time t or the initial condition.
- Type
- Research Article
- Information
- Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 143 , Issue 2 , April 2013 , pp. 253 - 268
- Copyright
- Copyright © Royal Society of Edinburgh 2013
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