Local and global well-posedness for dispersion generalized Benjamin-Ono equations on the circle. (English) Zbl 1441.35007
Summary: New local well-posedness results for dispersion generalized Benjamin-Ono equations are proved in the periodic case. The family of equations under consideration links the Benjamin-Ono and Korteweg-de Vries equation. For sufficiently strong dispersion global well-posedness in \(L^2 (\mathbb{T} )\) is derived.
MSC:
| 35A01 | Existence problems for PDEs: global existence, local existence, non-existence |
| 35B10 | Periodic solutions to PDEs |
| 35R11 | Fractional partial differential equations |
Keywords:
dispersive equations; short-time Fourier restriction norm method; modified energies; periodic boundary conditionsReferences:
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