Université de Cergy-Pontoise

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19932020

most citedEpitaxial Growth of a Silicene Sheet

1.4k citations

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

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37 papers · 1 filter

math.AP2019★ 21 cited

Exterior energy bounds for the critical wave equation close to the ground state

Thomas Duyckaerts, Carlos E. Kenig, Frank Merle

By definition, the exterior asymptotic energy of a solution to a wave equation on $R^{1 + N}$ is the sum of the limits as $t \to \pm \infty$ of the energy in the the exterior…

math.AP2019★ 19 cited

Time optimal observability for Grushin Schrödinger equation

Nicolas Burq, Chenmin Sun

We consider two dimensional Grushin Schrödinger equation posed on a finite cylinder $Ω=(-1,1)_x\times \T_y$ with Dirichlet boundary condition. We obtain the sharp observability by…

math.AP2019

New examples of probabilistic well-posedness for nonlinear wave equations

Chenmin Sun, Nikolay Tzvetkov

We consider fractional wave equations with exponential or arbitrary polynomial nonlinearities. We prove the global well-posedness on the support of the corresponding Gibbs measures…

math.AP2018★ 23 cited

Transport of gaussian measures by the flow of the nonlinear Schrödinger equation

F. Planchon, N. Tzvetkov, N. Visciglia

We prove a new smoothing type property for solutions of the 1d quintic Schrödinger equation. As a consequence, we prove that a family of natural gaussian measures are quasi-invaria…

math.AP2018★ 2 cited

Low regularity blowup solutions for the mass-critical NLS in higher dimensions

Chenmin Sun, Jiqiang Zheng

In this paper, we study the $H^{s}$ -stability of the log-log blowup regime (which has been completely described in a series of recent works by Merle and Raphael) for the focusing mas…

math.AP2018

Remark on the semilinear ill-posedness for a periodic higher order KP-I equation

Tristan Robert

We prove that, for some irrational torus, the flow map of the periodic fifth-order KP-I equation is not locally uniformly continuous on the energy space, even on the hyperplanes of…

math.AP2017★ 19 cited

Inelasticity of soliton collisions for the 5D energy critical wave equation

Yvan Martel, Frank Merle

For the focusing energy critical wave equation in 5D, we construct a solution showing the inelastic nature of the collision of any two solitons, except the special case of two soli…

math.AP2017★ 4 cited

Random data wave equations

Nikolay Tzvetkov

Nowadays we have many methods allowing to exploit the regularising properties of the linear part of a nonlinear dispersive equation (such as the KdV equation, the nonlinear wave or…

math.AP2016

A modulation technique for the blow-up profile of the vector-valued semilinear wave equation

Asma Azaiez, Hatem Zaag

We consider a vector-valued blow-up solution with values in $R^{m}$ for the semilinear wave equation with power nonlinearity in one space dimension (this is a system of PDEs…

math.AP2016★ 41 cited

On the growth of Sobolev norms for NLS on $2 d$ and $3 d$ manifolds

Fabrice Planchon, Nikolay Tzvetkov, Nicola Visciglia

Using suitable modified energies we study higher order Sobolev norms' growth in time for the nonlinear Schrödinger equation (NLS) on a generic $2 d$ or $3 d$ compact manifold. In $2d…

math.AP2016★ 42 cited

Dynamics near the ground state for the energy critical nonlinear heat equation in large dimensions

Charles Collot, Frank Merle, Pierre Raphael

We consider the energy critical semilinear heat equation $\partial_{t} u = Δ u + ∣ u ∣^{\frac{4}{d - 2}} u, x \in R^{d}$ and give a complete classification of the flow near the groun…

math.AP2016★ 13 cited

Invariant measure and long time behavior of regular solutions of the Benjamin-Ono equation

Mouhamadou Sy

The Benjamin-Ono equation describes the propagation of internal waves in a stratified fluid. In the present work, we study large time dynamics of its regular solutions via some pro…

math.AP2015★ 35 cited

Construction of multi-solitons for the energy-critical wave equation in dimension 5

Yvan Martel, Frank Merle

We construct 2-solitons of any speed of the focusing energy-critical nonlinear wave equation in dimension 5. The existence result also holds for the case of K-solitons, for any K >…

math.AP2015★ 21 cited

Codimension one threshold manifold for the critical gKdV equation

Yvan Martel, Frank Merle, Kenji Nakanishi +1

We construct the 'threshold manifold' near the soliton for the mass critical gKdV equation, completing results obtained in arXiv:1204.4625 and arXiv:1204.4624. In a neighborhood of…

math.AP2014

On the interpolation with the potential bound for global solutions of the defocusing cubic wave equation on T2

Tristan Roy

We prove that the solutions of the defocusing cubic wave equation on T2 exist globally in time in Hs(T2) for s > 2/5 by contradiction. Assuming that one of the maximal times of exi…

math.AP2014★ 33 cited

Invariant measures and long time behaviour for the Benjamin-Ono equation III

Y. Deng, N. Tzvetkov, N. Visciglia

We complete the program developed in our previous works aiming to construct an infinite sequence of invariant measures of gaussian type associated with the conservation laws of the…

math.AP2013★ 62 cited

On the stability of the notion of non-characteristic point and blow-up profile for semilinear wave equations

Frank Merle, Hatem Zaag

We consider a blow-up solution for the semilinear wave equation in $N$ dimensions, with subconformal power nonlinearity. Introducing $\RR_0$ the set of non-characteristic points wi…

math.AP2013

Effective multiplicity for the Einstein-scalar field Lichnerowicz equation

Bruno Premoselli

We prove the stability of the Einstein-scalar field Lichnerowicz equation under subcritical perturbations of the critical nonlinearity in dimensions 3, 4 and 5. As a consequence, w…

math.AP2013★ 18 cited

The Einstein-scalar field constraint system in the positive case

Bruno Premoselli

We prove the existence of solutions to the conformal Einstein-scalar constraint system of equations for closed compact Riemannian manifolds in the positive case. Our results apply…

math.AP2012★ 3 cited

Gelfand-Shilov smoothing properties of the radially symmetric spatially homogeneous Boltzmann equation without angular cutoff

Nicolas Lerner, Yoshinori Morimoto, Karel Pravda-Starov +1

We prove that the Cauchy problem associated to the radially symmetric spatially homogeneous non-cutoff Boltzmann equation with Maxwellian molecules enjoys the same Gelfand-Shilov r…

math.AP2012★ 4 cited

A lower bound on the blow-up rate for the Davey-Stewartson system on the torus

Nicolas Godet

We consider the hyperbolic-elliptic version of the Davey-Stewartson system with cubic nonlinearity posed on the two dimensional torus. A natural setting for studying blow up soluti…

math.AP2012★ 12 cited

Dynamical Ionization Bounds for Atoms

Enno Lenzmann, Mathieu Lewin

We study the long-time behavior of the 3-dimensional repulsive nonlinear Hartree equation with an external attractive Coulomb potential $- Z /∣ x ∣$ , which is a nonlinear model for the…

math.AP2012★ 7 cited

Consequences of the choice of a particular basis of $L^{2} (S^{3})$ for the cubic wave equation on the sphere and the Euclidian space

Anne-Sophie de Suzzoni

In this paper, the almost sure global well-posedness of the cubic non linear wave equation on the sphere is studied when the initial datum is a random variable with values in low r…

math.AP2012★ 32 cited

The NLS ground states on product spaces

Susanna Terracini, Nikolay Tzvetkov, Nicola Visciglia

We study the nature of the Nonlinear Schrödinger equation ground states on the product spaces $R^{n} \times M^{k}$ , where $M^{k}$ is a compact Riemannian manifold. We prove that for smal…