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Walid Abou Salem

Publications and source records attributed to Walid Abou Salem.

4 recordsLinked to original sources
arXiv2014

Arrest of blowup for the 3-D semi-relativistic Schrödinger-Poisson system with pseudo-relativistic diffusion

We show global well-posedness in energy norm of the semi-relativistic Schrödinger-Poisson system of equations with attractive Coulomb interaction in ${\mathbb R}^3$ in the presence of pseudo-relativistic diffusion. We also discuss sufficient conditions to have well-posedness in ${\mathcal L}^2$. In the absence of dissipation, we show that the solution corresponding to an initial condition with negative energy blows up in finite time, which is as expected, since the nonlinearity is critical.

math-ph↗
arXiv2012

On the generalized semi-relativistic Schrödinger-Poisson system in R^n

The Cauchy problem for the semi-relativistic Schrödinger-Poisson system of equations is studied in ${\mathbb R}^n$, $n\geq 1$, for a wide class of nonlocal interactions. Furthermore, the asymptotic behavior of the solution as the mass tends to infinity is rigorously discussed, which corresponds to a non-relativistic limit.

math-ph↗
arXiv2012

Existence and nonlinear stability of stationary states for the semi-relativistic Schrödinger-Poisson system

We study the stationary states of the semi-relativistic Schrödinger-Poisson system in the repulsive (plasma physics) Coulomb case. In particular, we establish the existence and the nonlinear stability of a wide class of stationary states by means of the energy-Casimir method. We generalize the global well-posedness result of our previous work for the semi-relativistic Schrödinger-Poisson system to spaces with higher regularity.

math-ph↗