Low regularity well-posedness for KP-I equations: the dispersion-generalized case

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...

Well-posedness and Regularity of Generalized Navier-stokes Equations in Some Critical Q−spaces

We study the well-posedness and regularity of the generalized Navier-Stokes equations with initial data in a new critical space Q α;∞ (R ) = ∇ · (Qα(R )), β ∈ ( 1 2 , 1) which is larger than some known critical homogeneous Besov spaces. Here Qα(R ) is a space defined as the set of all measurable functions with sup(l(I)) Z

Ill-Posedness for Semilinear Wave Equations with Very Low Regularity

In this paper, we study the ill-posdness of the Cauchy problem for semilinear wave equation with very low regularity, where the nonlinear term depends on u and ∂tu. We prove a ill-posedness result for the “defocusing” case, and give an alternative proof for the supercritical “focusing” case, which improves the result in [4].

Low regularity solutions of the Benjamin-Ono and the KP-I equations

Numerical Simulation of Generalized Kp Type Equations with Small Dispersion

We numerically study nonlinear dispersive wave equations of generalized Kadomtsev-Petviashvili type in the regime of small dispersion. To this end we include general power-law nonlinearities with different signs. A particular focus is on the Korteweg-de Vries sector of the corresponding solutions. version: October 26, 2006