BAO-ZHU GUO, ZHI-CHAO SHAO, ON WELL-POSEDNESS, REGULARITY AND EXACT CONTROLLABILITY FOR PROBLEMS OF TRANSMISSION OF PLATE EQUATION WITH VARIABLE COEFFICIENTS, Quarterly of Applied Mathematics, Vol. 65 ...

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 ...

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 ...

In parallel, studies have demonstrated that optimal decay rates and well-posedness results can be achieved even without the customary smallness assumptions on the low-frequency components of the ...

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 $\Phi^4 ...

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 ...