In this paper, we derive a new formulation of the water waves equations with vorticity that generalizes the well-known Zakharov-Craig-Sulem formulation used in the irrotational case. We prove the ...

J. Colliander, M. Keel, G. Staffilani, H. Takaoka, T. Tao, Global Well-Posedness and Scattering for the Energy-Critical Nonlinear Schrödinger Equation in ℝ³ ...

This talk focuses on the well-posedness of the derivative nonlinear Schrödinger equation on the line. This model is known to be completely integrable and L^2 -critical with respect to scaling. However ...

The study of Korteweg–de Vries (KdV) type equations has progressed significantly, particularly in understanding the analytic properties of their solutions and the framework of well-posedness ...

Well-posedness: A condition for a mathematical problem that ensures the existence, uniqueness, and continuous dependence of solutions on initial conditions.

On the global well-posedness of singular SPDEs The goal of these lectures is to study the global well-posedness of singular SPDEs. As a warm-up, we first prove the global well-posedness of the Φ4 2 Φ ...