We prove the invariance of the Gibbs measure under the dynamics of the three-dimensional
cubic wave equation, which is also known as the hyperbolic Φ 3 4-model. This result is the …

Invariant Gibbs measures for the three-dimensional wave equation with a Hartree nonlinearity
II: Dynamics Page 1 © 2023 European Mathematical Society Published by EMS Press and …

In this paper we discuss quantitative (pointwise) decay estimates for solutions to the 3D
cubic defocusing nonlinear Schrödinger equation with various (deterministic and random) …

In this paper, the general solutions of five important mathematical physics equations are
obtained for the first time, using the Z transformations that we have previously proposed …

Abstract We discuss the (1+ 1)-dimensional wave maps equation with values in a compact
Riemannian manifold. Motivated by the Gibbs measure problem, we consider Brownian …

We study the random data problem for 3D, defocusing, cubic nonlinear Schrödinger
equation in H xs (R 3) with s< 1 2. First, we prove that the almost sure local well-posedness …

We consider the focusing energy-critical quintic nonlinear wave equation in 3D Euclidean
space. It is known that this equation admits a one-parameter family of radial stationary …

We study the cubic defocusing nonlinear Schrödinger equation on R 4 with supercritical
initial data. For randomized initial data in H s (R 4), we prove almost sure local …

In this paper, we study the defocusing energy-critical nonlinear Schr\" odinger equations $$
i\partial_t u+\Delta u=| u|^{\frac {4}{d-2}} u. $$ When $ d= 3, 4$, we prove the almost sure …

We consider the radial nonlinear Schr\" odinger equation $ i\partial_tu+\Delta u=| u|^{p-1} u
$ in dimension $ d\geqslant 2$ for $ p\in\left (1, 1+\frac {4}{d}\right] $ and construct a natural …