The Hunter–Saxton equation with noise

Langevin equation with super-heavy-tailed noise

We extend the Langevin approach to a class of driving noises whose generating processes have independent increments with super-heavy-tailed distributions. The time-dependent generalized Fokker–Planck equation that corresponds to the first-order Langevin equation driven by such a noise is derived and solved exactly. This noise generates two probabilistic states of the system, survived and absorb...

Stochastic heat equation with white-noise drift

Langevin equation with scale - dependent noise

A new wavelet based technique for the perturbative solution of the Langevin equation is proposed. It is shown that for the random force acting in a limited band of scales the proposed method directly leads to a finite result with no renormalization required. The one-loop contribution to the Kardar-Parisi-Zhang equation Green function for the interface growth is calculated as an example. The Lan...

The nonlinear Schrödinger equation with white noise dispersion

Under certain scaling the nonlinear Schrödinger equation with random dispersion converges to the nonlinear Schrödinger equation with white noise dispersion. The aim of this work is to prove that this latter equation is globally well posed in L or H. The main ingredient is the generalization of the classical Strichartz estimates. Additionally, we justify rigorously the formal limit described abo...

The Schrödinger equation with spatial white noise potential

We consider the linear and nonlinear Schrödinger equation with a spatial white noise as a potential in dimension 2. We prove existence and uniqueness of solutions thanks to a change of unknown originally used in [8] and conserved quantities. 2010 Mathematics Subject Classification AMS: