On nonlinear dispersive equations.
Local existence theory for the generalized Schrödinger equation
On the Davey-Stewartson systems
Well-posedness of the Euler and Navier-Stokes equations in the Lebesque spaces L (R).
In this paper we show that the Euler equation for incompressible fluids in R2 is well posed in the (vector-valued) Lebesgue spaces Ls p = (1 - ∆)-s/2 Lp(R2) with s > 1 + 2/p, 1 < p < ∞ and that the same is true of the Navier-Stokes equation uniformly in the viscosity ν.
The local ill-posedness of the modified KdV equation
On the support of solutions to the generalized KdV equation
Small solutions to nonlinear Schrödinger equations
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