307 citations · 1.2k across the 45 of their papers we have counts for
46 papers
Equilibria for the Vlasov-Maxwell system related to plasma confinement
Justin Holmer, Katherine Zhiyuan Zhang
By working in a setting of azimuthal and -directional invariance, we reduce the existence of electrically neutral, magnetically driven, equilibria of the two-species Vlasov-Maxw…
The Derivation of the Boltzmann Equation from Quantum Many-body Dynamics
Xuwen Chen, Justin Holmer
We consider the quantum many-body dynamics at the weak-coupling scaling. We derive rigorously the quantum Boltzmann equation, which contains the classical hard sphere model and, ef…
Well/ill-posedness bifurcation for the Boltzmann equation with constant collision kernel
Xuwen Chen, Justin Holmer
We consider the 3D Boltzmann equation with the constant collision kernel. We investigate the well/ill-posedness problem using the methods from nonlinear dispersive PDEs. We constru…
Benjamin-Ono Soliton Dynamics in a slowly varying potential revisited
Justin Holmer, Katherine Zhiyuan Zhang
The Benjamin Ono equation with a slowly varying potential is with , , and $W\in C_c^\infty(\mat…
Quantitative Derivation and Scattering of the 3D Cubic NLS in the Energy Space
Xuwen Chen, Justin Holmer
We consider the derivation of the defocusing cubic nonlinear Schrödinger equation (NLS) on from quantum -body dynamics. We reformat the hierarchy approach with…
The Unconditional Uniqueness for the Energy-critical Nonlinear Schrödinger Equation on
Xuwen Chen, Justin Holmer
We consider the cubic NLS which is energy-critical. We study the unconditional uniqueness of solution to the NLS via the cubic Gross-Pitaevskii hierarchy, an uncom…