Enhanced existence time of solutions to evolution equations of Whitham type
Abstract
We show that Whitham type equations ut + u ux -L ux = 0, where L is a general Fourier multiplier operator of order α ∈ [-1,1], α≠ 0, allow for small solutions to be extended beyond their expected existence time. The result is valid for a range of quadratic dispersive equations with inhomogeneous symbols in the dispersive range given by α, and should be extendable to other equations of the same relative dispersive strength.
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