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• W2938234269 abstract "We consider the Cauchy problem [ partial_t u+upartial_x u+L(partial_x u) =0, quad u(0,x)=u_0(x) ] for a class of Fourier multiplier operators $L$, and prove that the solution map $u_0mapsto u(t)$ is not uniformly continuous in $H^s$ on the real line or on the torus for $s > frac{3}{2}$. Under certain assumptions, the result also hold for $s > 0$. The class of equations considered includes in particular the Whitham equation and fractional Korteweg-de Vries equations and we show that, in general, the flow map cannot be uniformly continuous if the dispersion of $L$ is weaker than that of the KdV operator. The result is proved by constructing two sequences of solutions converging to the same limit at the initial time, while the distance at a later time is bounded below by a positive constant." @default.
• W2938234269 created "2019-04-25" @default.
• W2938234269 creator A5012140544 @default.
• W2938234269 date "2019-05-01" @default.
• W2938234269 modified "2023-09-24" @default.
• W2938234269 title "Non-uniform dependence on initial data for equations of Whitham type" @default.
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• W2938234269 doi "https://doi.org/10.57262/ade/1554256825" @default.
• W2938234269 hasPublicationYear "2019" @default.
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