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- W2950304772 abstract "We establish the local well-posedness of the generalized Benjamin-Ono equation $partial_tu+mathcal{H}partial_x^2upm u^kpartial_xu=0$ in $H^s(R)$, $s>1/2-1/k$ for $kgeq 12$ and without smallness assumption on the initial data. The condition $s>1/2-1/k$ is known to be sharp since the solution map $u_0mapsto u$ is not of class $mathcal{C}^{k+1}$ on $H^s(R)$ for $s<1/2-1/k$. On the other hand, in the particular case of the cubic Benjamin-Ono equation, we prove the ill-posedness in $H^s(R)$, $s<1/3$." @default.
- W2950304772 created "2019-06-27" @default.
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- W2950304772 date "2007-03-21" @default.
- W2950304772 modified "2023-09-27" @default.
- W2950304772 title "Sharp well-posedness results for the generalized Benjamin-Ono equation with high nonlinearity" @default.
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