81 citations · 160 across the 37 of their papers we have counts for
27 papers · 1 filter
Entropy and Fisher information in non-convex domains: one chain to rule them all
Jean-Baptiste Casteras, Marco Flaim, Léonard Monsaingeon
We prove that the (square root) Fisher information functional is a strong Wasserstein upper gradient of the entropy on non-convex Riemannian domains. This fills a gap in the litera…
New invariant surface measures for the cubic Schrödinger equation
Jean-Baptiste Casteras, Ana Bela Cruzeiro, Annie Millet
We construct new invariant measures supported on mass level sets for the cubic defocusing nonlinear Schrödinger equation in dimensions and .
Large deviations for sticky-reflecting Brownian motion with boundary diffusion
Jean-Baptiste Casteras, Leonard Monsaingeon, Luca Nenna
We study a Schilder-type large deviation principle for sticky-reflected Brownian motion with boundary diffusion, both at the static and sample path level in the short-time limit. A…
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 …
Sticky-reflecting diffusion as a Wasserstein gradient flow
Jean-Baptiste Casteras, Léonard Monsaingeon, Filippo Santambrogio
In this paper we identify the Fokker-Planck equation for (reflected) Sticky Brownian Motion as a Wasserstein gradient flow in the space of probability measures. The driving functio…
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…
On the existence and partial stability of standing waves for a nematic liquid crystal director field equation
Paulo Amorim, Jean-Baptiste Casteras, João Paulo Dias
In this paper, following the studies of Amorim and al. in Partial Differ.Equ. Appl. '23, we consider some new aspects of the motion of the director field of a nematic liquid crysta…
Construction of 2-bubbles for the energy critical bi-harmonic Schrödinger equation
Jean-Baptiste Casteras, Ilkka Holopainen, Léonard Monsaingeon
We construct a blowing-up solution for the energy critical focusing biharmonic nonlinear Schrödinger equation in infinite time in dimension . Our solution is radially sym…
Classification of radial blow-up at the first critical exponent for the Lin-Ni-Takagi problem in the ball
Denis Bonheure, Jean-Baptiste Casteras, Bruno Premoselli
We investigate the behaviour of radial solutions to the Lin-Ni-Takagi problem in the ball for : \begin{equation*} \left \{ \begin{aligned} - \tr…
Hidden dissipation and convexity for Kimura equations
Jean-Baptiste Casteras, Léonard Monsaingeon
In this paper we establish a rigorous gradient flow structure for one-dimensional Kimura equations with respect to some Wasserstein-Shahshahani optimal transport geometry. This is…
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…
Invariant measures and global well-posedness for a fractional Schrödinger equation with Moser-Trudinger type nonlinearity
Jean-Baptiste Casteras, Léonard Monsaingeon
In this paper, we construct invariant measures and global-in-time solutions for a fractional Schr\" odinger equation with a Moser-Trudinger type nonlinearity $$ i\partial_t u= (-Δ)…
Fourth order Schrödinger equation with mixed dispersion on certain Cartan-Hadamard manifolds
Jean-Baptiste Casteras, Ilkka Holopainen
We study the fourth order Schrödinger equation with mixed dispersion on an -dimensional Cartan-Hadamard manifold. At first, we focus on the case of the hyperbolic space. Using t…
Existence of traveling waves for a fourth order Schr\" odinger equation with mixed dispersion in the Helmholtz regime
Jean-Baptiste Casteras, Juraj Foldes
In this paper, we study the existence of traveling waves for a fourth order Schr\" odinger equations with mixed dispersion, that is, solutions to $$Δ^2 u +βΔu +i V \nabla u +αu =|u…
Bifurcation analysis of the Hardy-Sobolev equation
Denis Bonheure, Jean-Baptiste Casteras, Francesca Gladiali
In this paper, we prove existence of multiple non-radial solutions to the Hardy-Sobolev equation $$\begin{cases} -Δu-\displaystyle\frac γ{|x|^2}u=\displaystyle\frac{1}{|x|^s}|u|^{p…
Singular radial solutions for the Lin-Ni-Takagi equation
Juraj Foldes, Jean-Baptiste Casteras
We study singular radially symmetric solution to the Lin-Ni-Takagi equation for a supercritical power non-linearity in dimension . It is shown that for any ball and any $k…
Construction of a solution for the two-component radial Gross-Pitaevskii system with a large coupling parameter
Jean-Baptiste Casteras, Christos Sourdis
We consider strongly coupled competitive elliptic systems that arise in the study of two-component Bose-Einstein condensates. As the coupling parameter tends to infinity, solutions…
On Helmholtz equations and counterexamples to Strichartz estimates in hyperbolic space
Jean-Baptiste Casteras, Rainer Mandel
In this paper, we study nonlinear Helmholtz equations (NLH) in , where d…
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 a fourth order nonlinear Helmholtz equation
Denis Bonheure, Jean-Baptiste Casteras, Rainer Mandel
In this paper, we study the mixed dispersion fourth order nonlinear Helmholtz equation in for positive, bounded and -peri…
Normalized solutions to the mixed dispersion nonlinear Schrödinger equation in the mass critical and supercritical regime
Denis Bonheure, Jean-Baptiste Casteras, Tianxiang Gou +1
In this paper, we study the existence of solutions to the mixed dispersion nonlinear Schrödinger equation under the constr…
Orbitally stable standing waves of a mixed dispersion nonlinear Schrödinger equation
Denis Bonheure, Jean-Baptiste Castéras, Ederson Moreira dos Santos +1
We study the mixed dispersion fourth order nonlinear Schrödinger equation \begin{equation*} %\tag{\protect{4NLS}}\label{4nls} i \partial_t ψ-γΔ^2 ψ+βΔψ+|ψ|^{2σ} ψ=0\ \text{in}\ \R…
Unbounded mass radial solutions for the Keller-Segel equation in the disk
Denis Bonheure, Jean-Baptiste Casteras, Carlos Román
We consider the boundary value problem $$ \left\{ \begin{array}{rcll} -Δu+ u -λe^u&=&0,\ u>0 & \mathrm{in}\ B_1(0)\\ \partial_νu&=&0&\mathrm{on}\ \partial B_1(0), \end{array}\right…
Strong instability of ground states to a fourth order Schrödinger equation
Denis Bonheure, Jean-Baptiste Casteras, Tianxiang Gou +1
In this note we prove the instability by blow-up of the ground state solutions for a class of fourth order Schr\" odinger equations. This extends the first rigorous results on blow…