Robin Ming Chen
University of Pittsburgh
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Featured researches published by Robin Ming Chen.
Communications in Partial Differential Equations | 2011
Robin Ming Chen; Yue Liu; Zhijun Qiao
We study here the existence of solitary wave solutions of a generalized two-component Camassa–Holm system. In addition to those smooth solitary-wave solutions, we show that there are solitary waves with singularities: peaked and cusped solitary waves. We also demonstrate that all smooth solitary waves are orbitally stable in the energy space. We finally give a sufficient condition for global strong solutions to the equation in some special case.
Proceedings of the Royal Society of London A: Mathematical, Physical and Engineering Sciences | 2009
Robin Ming Chen; Yujin Guo; Daniel Spirn; Yisong Yang
In this paper, we prove the existence of finite-energy electrically and magnetically charged vortex solutions in the full Chern–Simons–Higgs theory, for which both the Maxwell term and the Chern–Simons term are present in the Lagrangian density. We consider both Abelian and non-Abelian cases. The solutions are smooth and satisfy natural boundary conditions. Existence is established via a constrained minimization procedure applied on indefinite action functionals. This work settles a long-standing open problem concerning the existence of dually charged vortices in the classical gauge field Higgs model minimally extended to contain a Chern–Simons term.
Journal of Nonlinear Science | 2013
Robin Ming Chen; Jonatan Lenells; Yue Liu
The μ-Camassa–Holm (μCH) equation is a nonlinear integrable partial differential equation closely related to the Camassa–Holm equation. We prove that the periodic peaked traveling wave solutions (peakons) of the μCH equation are orbitally stable.
Nonlinearity | 2008
Robin Ming Chen; Vera Mikyoung Hur; Yue Liu
The rotation-modified Kadomtsev–Petviashvili equation describes small-amplitude, long internal waves propagating in one primary direction in a rotating frame of reference. The main investigation is the existence and properties of its solitary waves. The existence and nonexistence results for the solitary waves are obtained, and their regularity and decay properties are established. Various characterizations are given for the ground states and their cylindrical symmetry is demonstrated. When the effects of rotation are weak, the energy minima constrained by constant momentum are shown to be nonlinearly stable. The weak rotation limit of solitary waves as the rotation parameter tends to zero is studied.
Archive for Rational Mechanics and Analysis | 2016
Robin Ming Chen; Samuel Walsh
There are two distinct regimes commonly used to model traveling waves in stratified water: continuous stratification, where the density is smooth throughout the fluid, and layer-wise continuous stratification, where the fluid consists of multiple immiscible strata. The former is the more physically accurate description, but the latter is frequently more amenable to analysis and computation. By the conservation of mass, the density is constant along the streamlines of the flow; the stratification can therefore be specified by prescribing the value of the density on each streamline. We call this the streamline density function.Our main result states that, for every smoothly stratified periodic traveling wave in a certain small-amplitude regime, there is an L∞ neighborhood of its streamline density function such that, for any piecewise smooth streamline density function in that neighborhood, there is a corresponding traveling wave solution. Moreover, the mapping from streamline density function to wave is Lipschitz continuous in a certain function space framework. As this neighborhood includes piecewise smooth densities with arbitrarily many jump discontinues, this theorem provides a rigorous justification for the ubiquitous practice of approximating a smoothly stratified wave by a layered one. We also discuss some applications of this result to the study of the qualitative features of such waves.
Archive for Rational Mechanics and Analysis | 2018
Hong Cai; Geng Chen; Robin Ming Chen; Y. Shen
We consider the Lipschitz continuous dependence of solutions for the Novikov equation with respect to the initial data. In particular, we construct a Finsler type optimal transport metric which renders the solution map Lipschitz continuous on bounded sets of
Journal of Mathematical Fluid Mechanics | 2017
Robin Ming Chen; Vera Mikyoung Hur; Samuel Walsh
Transactions of the American Mathematical Society | 2012
Robin Ming Chen; Yue Liu; Pingzheng Zhang
{H^1(\mathbb{R})\cap W^{1,4}(\mathbb{R})}
Mathematical Models and Methods in Applied Sciences | 2015
M. Carme Calderer; Robin Ming Chen
International Mathematics Research Notices | 2010
Robin Ming Chen; Yue Liu
H1(R)∩W1,4(R), although it is not Lipschitz continuous under the natural Sobolev metric from an energy law due to the finite time gradient blowup. By an application of Thom’s transversality theorem, we also prove that when the initial data is in an open dense subset of