108 citations · 365 across the 21 of their papers we have counts for
14 papers · 1 filter
Bounds on the growth of high Sobolev norms of solutions to the fractional nonlinear Schrödinger equation on and
Antonios Kapetanios, José L. Rodrigo, Vedran Sohinger
We prove polynomial bounds on the growth of high Sobolev norms of solutions to the defocusing fractional nonlinear Schrödinger equation with cubic and Hartree-type nonlinearities i…
Gibbs measures as local equilibrium KMS states for focusing nonlinear Schrödinger equations
Zied Ammari, Andrew Rout, Vedran Sohinger
In this paper, we are concerned with the study of statistical equilibria for focusing nonlinear Schrödinger and Hartree equations on the d-dimensional torus when d=1,2,3. Due to th…
Almost sure existence of global solutions for general initial value problems
Zied Ammari, Shahnaz Farhat, Vedran Sohinger
This article is concerned with the almost sure existence of global solutions for initial value problems of the form on separable dual Banach spaces. We prove…
A microscopic derivation of Gibbs measures for nonlinear Schrödinger equations with unbounded interaction potentials
Vedran Sohinger
We study the derivation of the Gibbs measure for the nonlinear Schrödinger equation (NLS) from many-body quantum thermal states in the high-temperature limit. In this paper, we con…
Unconditional Uniqueness Results for the Nonlinear Schrödinger Equation
Sebastian Herr, Vedran Sohinger
We study the problem of unconditional uniqueness of solutions to the cubic nonlinear Schrödinger equation. We introduce a new strategy to approach this problem on bounded domains,…
The Gross-Pitaevskii hierarchy on general rectangular tori
Sebastian Herr, Vedran Sohinger
In this work, we study the Gross-Pitaevskii hierarchy on general --rational and irrational-- rectangular tori of dimension two and three. This is a system of infinitely many linear…
A rigorous derivation of the defocusing cubic nonlinear Schrödinger equation on from the dynamics of many-body quantum systems
Vedran Sohinger
In this paper, we will obtain a rigorous derivation of the defocusing cubic nonlinear Schrödinger equation on the three-dimensional torus from the many-body limit of…
Local existence of solutions to Randomized Gross-Pitaevskii hierarchies
Vedran Sohinger
In this paper, we study the local-in-time existence of solutions to randomized forms of the Gross-Pitaevskii hierarchy on periodic domains. In particular, we study the independentl…
Randomization and the Gross-Pitaevskii hierarchy
Vedran Sohinger, Gigliola Staffilani
We study the Gross-Pitaevskii hierarchy on the spatial domain . By using an appropriate randomization of the Fourier coefficients in the collision operator, we prove…
On the uniqueness of solutions to the periodic 3D Gross-Pitaevskii hierarchy
P. Gressman, V. Sohinger, G. Staffilani
In this paper, we present a uniqueness result for solutions to the Gross-Pitaevskii hierarchy on the three-dimensional torus, under the assumption of an a priori spacetime bound. W…
The Boltzmann equation, Besov spaces, and optimal time decay rates in the whole space
Vedran Sohinger, Robert M. Strain
We prove that -th order derivatives of perturbative classical solutions to the hard and soft potential Boltzmann equation (without the angular cut-off assumption) in the whole s…
Bounds on the growth of high Sobolev norms of solutions to 2D Hartree Equations
Vedran Sohinger
In this paper, we consider Hartree-type equations on the two-dimensional torus and on the plane. We prove polynomial bounds on the growth of high Sobolev norms of solutions to thes…
Bounds on the growth of high Sobolev norms of solutions to Nonlinear Schrodinger Equations on
Vedran Sohinger
In this paper, we consider the cubic nonlinear Schrodinger equation, and the Hartree equation, with sufficiently regular convolution potential, both on the real line. We are intere…
Bounds on the growth of high Sobolev norms of solutions to Nonlinear Schrodinger Equations on
Vedran Sohinger
We consider Nonlinear Schrodinger type equations on . In this paper, we obtain polynomial bounds on the growth in time of high Sobolev norms of their solutions. The key is to…