13 citations · 14 across the 12 of their papers we have counts for
14 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…
Stationary flows for viscous heat-conductive fluid in a perturbed half-space
Mingjie Li, Masahiro Suzuki, Katherine Zhiyuan Zhang
We consider the non-isentropic compressible Navier-Stokes equation in a perturbed half space with an outflow boundary condition as well as the supersonic condition. This equation m…
Local Well-posedness for the Kinetic MMT Model
Pierre Germain, Joonhyun La, Katherine Zhiyuan Zhang
The MMT equation was proposed by Majda, McLaughlin and Tabak as a model to study wave turbulence. We focus on the kinetic equation associated to this Hamiltonian system, which is b…
Traveling Waves of the Vlasov--Poisson System
Masahiro Suzuki, Masahiro Takayama, Katherine Zhiyuan Zhang
We consider the Vlasov--Poisson system describing a two-species plasma with spatial dimension and the velocity variable in . We find the necessary and sufficient…
Nonlinear Stability and Instability of Plasma Boundary Layers
Masahiro Suzuki, Masahiro Takayama, Katherine Zhiyuan Zhang
We investigate the formation of a plasma boundary layer (sheath) by considering the Vlasov--Poisson system on a half-line with the completely absorbing boundary condition. In an ea…
Solutions of the 2D Radially Symmetric Vlasov-Maxwell System with an Initial Focusing Phase
Katherine Zhiyuan Zhang
We study radially symmetric solutions to the 2D Vlasov-Maxwell system and construct solutions that initially possess arbitrarily small norms () for the charge densi…
On d quadratic Klein-Gordon equations with a potential and symmetries
Pierre Germain, Fabio Pusateri, Katherine Zhiyuan Zhang
This paper is a continuation of a previous work Germain-Pusateri (2020) by the first two authors. We focus on dimensional quadratic Klein-Gordon equations with a potential, und…
Effective Dynamics of the Vector Nonlinear Schrödinger Equations on Large Domains
Katherine Zhiyuan Zhang
We consider the vector nonlinear Schrödinger equation posed on the box with periodic boundary conditions, and derive the continuous resonant (CR) equation that describes the effect…
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…
Boundary layers of the Boltzmann equation in a three-dimensional half-space
Shota Sakamoto, Masahiro Suzuki, Katherine Zhiyuan Zhang
We consider the nonlinear boundary layers of the Boltzmann equation in a three-dimensional half-space by perturbing around a Maxwellian, under the assumption that the Mach number o…
Stationary flows for compressible viscous fluid in a perturbed half-space
Masahiro Suzuki, Katherine Zhiyuan Zhang
We consider the compressible Navier--Stokes equation in a perturbed half-space with an outflow boundary condition as well as the supersonic condition. For a half-space, it has been…
Benjamin-Ono Soliton Dynamics in a Slowly Varying Potential
Katherine Zhiyuan Zhang
We consider the Benjamin-Ono equation with a slowly varying potential with , , and , and $…
Focusing Solutions of the Vlasov-Poisson System
Katherine Zhiyuan Zhang
We study smooth, spherically-symmetric solutions to the Vlasov-Poisson system and relativistic Vlasov-Poisson system in the plasma physical case. We construct solutions that initia…
Linear Stability Analysis of the Relativistic Vlasov-Maxwell System in an Axisymmetric Domain
Katherine Zhiyuan Zhang
We consider the plasma confined in a general axisymmetric spatial domain with perfect conducting boundary which reflects particles specularly, and look at a certain class of equili…