307 citations · 1.2k across the 45 of their papers we have counts for
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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…
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…
Asymptotic stability of solitary waves of the 3D quadratic Zakharov-Kuznetsov equation
Luiz Gustavo Farah, Justin Holmer, Svetlana Roudenko +1
We consider the quadratic Zakharov-Kuznetsov equation on . A solitary wave solution is given by , w…