. A P ] 2 1 O ct 2 00 2 LOCAL WELL - POSEDNESS FOR DISPERSION GENERALIZED BENJAMIN - ONO EQUATIONS
نویسندگان
چکیده
In this paper we study local well-posedness in the energy space for a family of dispersive equations that can be seen as dispersive " interpolations " between the KdV and the Benjamin-Ono equation.
منابع مشابه
Local Well-posedness for Dispersion Generalized Benjamin-ono Equations in Sobolev Spaces
We prove that the Cauchy problem for the dispersion generalized Benjamin-Ono equation ∂tu+ |∂x| ∂xu+ uux = 0, u(x, 0) = u0(x), is locally well-posed in the Sobolev spaces H for s > 1 − α if 0 ≤ α ≤ 1. The new ingredient is that we develop the methods of Ionescu, Kenig and Tataru [13] to approach the problem in a less perturbative way, in spite of the ill-posedness results of Molinet, Saut and T...
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