5 papers
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…
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…
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…
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…