This paper studies the pressureless Euler-Poisson system and its fully non-linear counterpart , the Euler-Monge-Ampère system, where the fully non-linear Monge-Ampère equation substitutes for the linear Poisson equation. While the first is a model of plasma physics, the second is derived as a geometric approximation to the Euler incompressible equations. Using energy estimates, convergence of b...

This paper studies the pressureless Euler-Poisson system and its fully non-linear counterpart, the Euler-Monge-Ampère system, where the fully non-linear Monge-Ampère equation substitutes for the linear Poisson equation. While the first is a model of plasma physics, the second is derived as a geometric approximation to the Euler incompressible equations. Using energy estimates, convergence of bo...

The gauge freedom of the incompressible Euler equations is explored. We present various forms of the Euler equations written in terms of the impulse density. It is shown that these various forms are related by a gauge transformation. We devise a numerical method to solve the impulse form of the Euler equations in a variety of gauges. The numerical scheme is implemented both in two and three spa...

ABSTRACT. We extend a recent result on third and fourth-order Cauchy-Euler equations by establishing the Hyers-Ulam stability of higher-order linear non-homogeneous Cauchy-Euler dynamic equations on time scales. That is, if an approximate solution of a higher-order Cauchy-Euler equation exists, then there exists an exact solution to that dynamic equation that is close to the approximate one. We...

Copyright q 2012 J. Yang and Z. Zhuang. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. We rigorously justify a singular Euler-Poisson approximation of the incompressible Euler equations in the quasi-neutral regime for plasma phys...

In this paper, we are concerned with the Cauchy problem on the compressible isentropic two-fluids Euler-Maxwell equations in three dimensions. The global existence of solutions near constant steady states with the vanishing electromagnetic field is established, and also the time-decay rates of perturbed solutions in L space for 2 ≤ q ≤ ∞ are obtained. The proof for existence is due to the class...

Since completion of the Ph.D. program at California Institute of Technology, my research has been focused on application of methods of differential geometry and global analysis to the study of nonlinear partial differential equations. Specifically, it concerns • Euler and Euler-α equations of ideal fluid flow (both fixed and moving boundary case), • Camassa-Holm equation, • EPDiff equations (al...

Using the Hodge decomposition on bounded domains the compressible Euler equations of gas dynamics are reformulated using a density weighted vorticity and dilatation as primary variables, together with the entropy and density. This formulation is an extension to compressible flows of the well-known vorticity-stream function formulation of the incompressible Euler equations. The Hamiltonian and a...

We prove that there exists no self-similar finite time blowing up solution to the 3D incompressible Euler equations. The proof uses the vorticity transport formula represented in terms of the back to label map. By similar method we also show nonexistence of self-similar blowing up solutions to the divergence-free transport equation in R. This result has direct applications to the density depend...

We prove the global regularity for both of the 3D Navier-Stokes equations and the 3D Euler equations on R for initial data v0 ∈ H (R). 1 Main Result We are concerned on the following Navier-Stokes equations(Euler equations for ν = 0) describing the homogeneous incompressible fluid flows in R. (NS)ν 