5 papers · 1 filter
Higher order expansion for the probabilistic local well-posedness theory for a cubic nonlinear Schrödinger equation
Jean-Baptiste Casteras, Juraj Foldes, Gennady Uraltsev
In this paper, we study the probabilistic local well-posedness of the cubic Schrödinger equation (cubic NLS): \[ (i\partial_{t} + Δ) u = \pm |u|^{2} u \text{ on } [0,T) \times \mat…
Almost sure global well-posedness for 3D Euler equation and other fluid dynamics models
Juraj Foldes, Mouhamadou Sy
We construct various statistical ensembles associated to the 3D Euler equations and prove global regularity of these equations for data living on these sets. Similar results are al…
The method of stochastic characteristics for linear second-order hypoelliptic equations
Juraj Foldes, David Herzog
We study hypoelliptic stochastic differential equations (SDEs) and their connection to degenerate-elliptic boundary value problems on bounded or unbounded domains. In particular, w…
Existence of traveling waves for a fourth order Schr\" odinger equation with mixed dispersion in the Helmholtz regime
Jean-Baptiste Casteras, Juraj Foldes
In this paper, we study the existence of traveling waves for a fourth order Schr\" odinger equations with mixed dispersion, that is, solutions to $$Δ^2 u +βΔu +i V \nabla u +αu =|u…
Paths to uniqueness of critical points and applications to partial differential equations
Denis Bonheure, Juraj Földes, Ederson Moreira dos Santos +2
We prove a unified and general criterion for the uniqueness of critical points of a functional in the presence of constraints such as positivity, boundedness, or fixed mass. Our me…