École Normale Supérieure de Rennes

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20052025

most citedDegenerate parabolic stochastic partial differential equations: Quasilinear case

90 citations

researchers with a paper here

Counting papers with at most 25 authors, so collaboration author lists do not stand in for the people here.

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17 papers · 1 filter

math.AP2025

Blow-up, decay, and convergence to equilibrium for focusing damped cubic Klein-Gordon and Duffing equations

Thomas Perrin

We study long-time dynamics of the damped focusing cubic Klein-Gordon equation on a compact three-dimensional Riemannian manifold, together with its space-independent reduction, th…

math.AP2025

Small-time approximate controllability of the logarithmic Schr\''dinger equation

Karine Beauchard, Rémi Carles, Eugenio Pozzoli

We consider Schr{ö}dinger equations with logarithmic nonlinearity and bilinear controls, posed on $T^{d}$ or $R^{d}$ . We prove their small-time global $L^{2}$ -approxima…

math.AP2025

Small-time local control of a Schrödinger equation: a negative and a positive quadratic result

Karine Beauchard, Frédéric Marbach, Thomas Perrin

We study the small-time local controllability (STLC) of a bilinear Schrödinger equation with Neumann boundary conditions near its ground state. We focus on the degenerate case wher…

math.AP2024

Periodic nonlinear Schrödinger equation with distributional potential and invariant measures

Arnaud Debussche, Antoine Mouzard

In this paper, we continue some investigations on the periodic NLSE started by Lebowitz, Rose and Speer and by Bourgain with the addition of a distributional multiplicative potenti…

math.AP2022★ 14 cited

A consistent stochastic large-scale representation of the Navier-Stokes equations

Arnaud Debussche, Berenger Hug, Etienne Memin

In this paper we analyze the theoretical properties of a stochastic representation of the incompressible Navier-Stokes equations defined in the framework of the modeling under loca…

math.AP2021★ 1 cited

Invariant Gibbs measure for a Schrodinger equation with exponential nonlinearity

Tristan Robert

We investigate the invariance of the Gibbs measure for the fractional Schrodinger equation of exponential type (expNLS) $i \partial_{t} u + (- Δ)^{\frac{α}{2}} u = 2 γ β e^{β ∣ u ∣^{2}} u$ on $d$ -d…

math.AP2021

Heat equation on the Heisenberg group: observability and applications

Karine Beauchard, Piermarco Cannarsa

We investigate observability and Lipschitz stability for the Heisenberg heat equation on the rectangular domain $Ω = (- 1, 1) \times T \times T$ taking as observation…

math.AP2020★ 9 cited

Stochastic quantization of Liouville conformal field theory

Tadahiro Oh, Tristan Robert, Nikolay Tzvetkov +1

We study a nonlinear stochastic heat equation forced by a space-time white noise on closed surfaces, with nonlinearity $e^{β u}$ . This equation corresponds to the stochastic quantiz…

math.AP2016★ 2 cited

Null-controllability of non-autonomous Ornstein-Uhlenbeck equations

Karine Beauchard, Karel Pravda-Starov

We study the null-controllability of parabolic equations associated to non-autonomous Ornstein-Uhlenbeck operators. When a Kalman type condition holds for some positive time $T > 0$ ,…

math.AP2016★ 1 cited

Global wellposedness for a class of reaction-advection-anisotropic-diffusion systems

Dieter Bothe, André Fischer, Michel Pierre +1

We prove existence and uniqueness of global solutions for a class of reaction-advection-anisotropic-diffusion systems whose reaction terms have a "triangular structure". We thus ex…

math.AP2015

A transmission problem across a fractal self-similar interface

Yves Achdou, Thibaut Deheuvels

We consider a transmission problem in which the interior domain has infinitely ramified structures. Transmission between the interior and exterior domains occurs only at the fracta…

math.AP2014

Diffusion limit for the radiative transfer equation perturbed by a Markovian process

Arnaud Debussche, Sylvain De Moor, Julien Vovelle

We study the stochastic diffusive limit of a kinetic radiative transfer equation, which is non-linear, involving a small parameter and perturbed by a smooth random term. Under an a…

math.AP2014

Diffusion limit for the radiative transfer equation perturbed by a Wiener process

Arnaud Debussche, Sylvain De Moor, Julien Vovelle

The aim of this paper is the rigorous derivation of a stochastic non-linear diffusion equation from a radiative transfer equation perturbed with a random noise. The proof of the co…

math.AP2013★ 13 cited

Global existence for diffusion-electromigration systems in space dimension three and higher

Dieter Bothe, André Fischer, Michel Pierre +1

We prove existence of global weak solutions for the Nernst-Planck-Poisson problem which describes the evolution of concentrations of charged species $X_{1}, ..., X_{P}$ subject to Fick…

math.AP2013★ 24 cited

On the eigenvalues of Aharonov-Bohm operators with varying poles

Virginie Bonnaillie-Noël, Benedetta Noris, Manon Nys +1

We consider a magnetic operator of Aharonov-Bohm type with Dirichlet boundary conditions in a planar domain. We analyse the behavior of its eigenvalues as the singular pole moves i…

math.AP2013★ 90 cited

Degenerate parabolic stochastic partial differential equations: Quasilinear case

Arnaud Debussche, Martina Hofmanová, Julien Vovelle

In this paper, we study the Cauchy problem for a quasilinear degenerate parabolic stochastic partial differential equation driven by a cylindrical Wiener process. In particular, we…

math.AP2013★ 1 cited

Permeability through a perforated domain for the incompressible 2D Euler equations

Virginie Bonnaillie-Noël, Christophe Lacave, Nader Masmoudi

We investigate the influence of a perforated domain on the 2D Euler equations. Small inclusions of size $ε$ are uniformly distributed on the unit segment or a rectangle,…