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Well-posedness of the periodic dispersion-generalized Benjamin-Ono equation in the weakly dispersive regime (2305.05638v1)

Published 9 May 2023 in math.AP

Abstract: We study the dispersion-generalized Benjamin-Ono equation in the periodic setting. This equation interpolates between the Benjamin-Ono equation ($\alpha=1$) and the viscous Burgers' equation ($\alpha=0$). We obtain local well-posedness in $Hs$ for $s>3/2-\alpha$ and $\alpha\in(0,1)$ by using the short-time Fourier restriction method.

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