7 papers · 1 filter
Probabilistic well-posedness of generalized cubic nonlinear Schrödinger equations with strong dispersion using higher order expansions
Jean-baptiste Casteras, Juraj Földes, Itamar Oliveira +1
In this paper, we study the local well-posedness of the cubic Schrödinger equation …
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…
Almost sure local well-posedness for cubic nonlinear Schrodinger equation with higher order operators
Jean-Baptiste Casteras, Juraj Foldes, Gennady Uraltsev
In this paper, we study the local well-posedness of the cubic Schrödinger equation: \[ (i \partial_t - \mathscr{L}) u = \pm |u|^2 u \quad \text{ on } I \times \mathbb{R}^d, \] with…
Singular radial solutions for the Keller-Segel equation in high dimension
Denis Bonheure, Jean-Baptiste Casteras, Juraj Foldes
We study singular radially symmetric solution of the stationary Keller-Segel equation, that is, an elliptic equation with exponential nonlinearity, which is super-critical in dimen…
On higher integrability estimates for elliptic equations with singular coefficients
Juraj Földes, Tuoc Phan
In this note we establish existence and uniqueness of weak solutions of linear elliptic equation , where the matrix…
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…