arXiv subjects

Yilun Wu

Publications and source records attributed to Yilun Wu.

23 records · Page 2Linked to original sources

arXiv2017

Jost Solutions and the Direct Scattering Problem of the Benjamin--Ono Equation

In this paper, we present a rigorous study of the direct scattering problem that arises from the complete integrability of the Benjamin--Ono (BO) equation. In particular, we establish existence, uniqueness, and asymptotic properties of the Jost solutions to the scattering operator in the Fokas--Ablowitz inverse scattering transform (IST). Formulas relating different scattering coefficients are proven, together with their asymptotic behavior with respect to the spectral parameter. This work is an initial step toward the construction of general solutions to the BO equation by IST.

math.AP↗

arXiv2017

Steady States of Rotating Stars and Galaxies

A rotating continuum of particles attracted to each other by gravity may be modeled by the Euler-Poisson system. The existence of solutions is a very classical problem. Here it is proven that a curve of solutions exists, parametrized by the rotation speed, with a fixed mass independent of the speed. The rotation is allowed to vary with the distance to the axis. A special case is when the equation of state is $p=ρ^γ,\ 6/5<γ<2,\ γ\ne4/3$, in contrast to previous variational methods which have required $4/3 < γ$. The continuum of particles may alternatively be modeled microscopically by the Vlasov-Poisson system. The kinetic density is a prescribed function. We prove an analogous theorem asserting the existence of a curve of solutions with constant mass. In this model the whole range $(6/5,2)$ is allowed, including $γ=4/3$.

math.AP↗

arXiv2015

Simplicity and Finiteness of Discrete Spectrum of the Benjamin-Ono Scattering Operator

A spectral analysis is done on the $L$ operator of the Lax pair for the Benjamin-Ono equation. Simplicity and finiteness of the discrete spectrum are established as are needed for the Fokas and Ablowitz inverse scattering transform scheme. A crucial step in the simplicity proof is the discovery of a new identity connecting the $L^2$ norm of the eigenvector to its inner product with the scattering potential. The proof for finiteness is an extension of the ideas involved in the Birman-Schwinger bound for Schrödinger operators.

math.AP↗

arXiv2014

On rotating star solutions to non-isentropic Euler-Poisson equations

This paper investigates rotating star solutions to the Euler-Poisson equations with a non-isentropic equation of state. As a first step, the equation for gas density with a prescribed entropy and angular velocity distribution is studied. The resulting elliptic equation is solved either by the method of sub and supersolutions or by a variational method, depending on the value of the adiabatic index. The reverse problem of determining angular velocity from gas density is also considered.

math-ph↗

arXiv2014

Existence of rotating planet solutions to the Euler-Poisson equations with an inner hard core

The Euler-Poisson equations model rotating gaseous stars. Numerous efforts have been made to establish existence and properties of the rotating star solutions. Recent interests in extrasolar planet structures require extension of the model to include a inner rocky core together with its own gravitational potential. In this paper, we discuss various extensions of the classical rotating star results to incorporate a solid core.

math.AP↗