8 citations · 38 across the 16 of their papers we have counts for
18 papers
Modulated logarithmic Sobolev inequalities and generation of chaos
Matthew Rosenzweig, Sylvia Serfaty
We consider mean-field limits for overdamped Langevin dynamics of particles with possibly singular interactions. It has been shown that a modulated free energy method can be us…
Trend to equilibrium for flows with random diffusion
Shrey Aryan, Matthew Rosenzweig, Gigliola Staffilani
Motivated by the possibility of noise to cure equations of finite-time blowup, recent work arXiv:2109.09892 by the second and third named authors showed that with quantifiable high…
Sharp uniform-in-time mean-field convergence for singular periodic Riesz flows
Antonin Chodron de Courcel, Matthew Rosenzweig, Sylvia Serfaty
We consider conservative and gradient flows for -particle Riesz energies with mean-field scaling on the torus , for , and with thermal noise of McKean-Vla…
A rigorous derivation of the Hamiltonian structure for the Vlasov equation
Joseph K. Miller, Andrea R. Nahmod, Nataša Pavlović +2
We consider the Vlasov equation in any spatial dimension, which has long been known to be an infinite-dimensional Hamiltonian system whose bracket structure is of Lie-Poisson type.…
From Quantum Many-Body Systems to Ideal Fluids
Matthew Rosenzweig
We give a rigorous, quantitative derivation of the incompressible Euler equation from the many-body problem for bosons on with binary Coulomb interactions in the…
Global solutions of aggregation equations and other flows with random diffusion
Matthew Rosenzweig, Gigliola Staffilani
Aggregation equations, such as the parabolic-elliptic Patlak-Keller-Segel model, are known to have an optimal threshold for global existence vs. finite-time blow-up. In particular,…
Global-in-time mean-field convergence for singular Riesz-type diffusive flows
Matthew Rosenzweig, Sylvia Serfaty
We consider the mean-field limit of systems of particles with singular interactions of the type or , with , and with an additive noise in dimensions…
Mean-field limits of Riesz-type singular flows
Quoc Hung Nguyen, Matthew Rosenzweig, Sylvia Serfaty
We provide a proof of mean-field convergence of first-order dissipative or conservative dynamics of particles with Riesz-type singular interaction (the model interaction is an inve…
On the Rigorous Derivation of the Incompressible Euler Equation from Newton's Second Law
Matthew Rosenzweig
A longstanding problem in mathematical physics is the rigorous derivation of the incompressible Euler equation from Newtonian mechanics. Recently, Han-Kwan and Iacobelli arXiv:2006…
Uniqueness of Solutions to the Spectral Hierarchy in Kinetic Wave Turbulence Theory
Matthew Rosenzweig, Gigliola Staffilani
In arXiv:1201.4067 and arXiv:1611.08030, Eyink and Shi and Chibbaro et al., respectively, formally derived an infinite, coupled hierarchy of equations for the spectral correlation…
The Mean-Field Limit of Stochastic Point Vortex Systems with Multiplicative Noise
Matthew Rosenzweig
In arXiv:1004.1407, Flandoli, Gubinelli, and Priola proposed a stochastic variant of the classical point vortex system of Helmholtz and Kirchoff in which multiplicative noise of tr…
Mean-Field Convergence of Systems of Particles with Coulomb Interactions in Higher Dimensions without Regularity
Matthew Rosenzweig
We consider first-order conservative systems of particles with binary Coulomb interactions in the mean-field scaling regime in dimensions . We show that if at some time, t…
Mean-Field Convergence of Point Vortices without Regularity
Matthew Rosenzweig
We consider the classical point vortex model in the mean-field scaling regime, in which the velocity field experienced by a single point vortex is proportional to the average of th…
The Mean-Field Limit of the Lieb-Liniger Model
Matthew Rosenzweig
We consider the well-known Lieb-Liniger (LL) model for bosons interacting pairwise on the line via the -potential in the mean-field scaling regime. Assuming suitable asympto…
Poisson Commuting Energies for a System of Infinitely Many Bosons
Dana Mendelson, Andrea R. Nahmod, Nataša Pavlović +2
We consider the cubic Gross-Pitaevskii (GP) hierarchy in one spatial dimension. We establish the existence of an infinite sequence of observables such that the corresponding trace…
A Rigorous Derivation of the Hamiltonian Structure for the Nonlinear Schrödinger Equation
Dana Mendelson, Andrea R. Nahmod, Nataša Pavlović +2
We consider the cubic nonlinear Schrödinger equation (NLS) in any spatial dimension, which is a well-known example of an infinite-dimensional Hamiltonian system. Inspired by the kn…
Justification of the Point Vortex Approximation for Modified Surface Quasi-Geostrophic Equations
Matthew Rosenzweig
In this paper, we give a rigorous justification of the point vortex approximation to the family of modified surface quasi-geostrophic (mSQG) equations globally in time in both the…
Global Well-Posedness and Scattering for the Elliptic-Elliptic Davey-Stewartson System at -Critical Regularity
Matthew Rosenzweig
In this paper, we prove global well-posedness and scattering of the Cauchy problem for the elliptic-elliptic Davey-Stewartson system (eeDS) for initial data $u_{0}\in L^{2}(\mathbb…