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- Title
Arrest of blow up for the 3D semi-relativistic Schrödinger-Poisson system with pseudo-relativistic diffusion.
- Authors
Abou Salem, W.; Chen, T.; Vougalter, V.
- Abstract
We show global well-posedness in energy norm of the semi-relativistic Schrödinger-Poisson system of equations with attractive Coulomb interaction in in the presence of pseudo-relativistic diffusion. We also discuss sufficient conditions to have well-posedness in . 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.
- Subjects
SCHRODINGER equation; POISSON'S equation; COULOMB'S law; MATHEMATICAL models of diffusion; NONLINEAR theories
- Publication
Reviews in Mathematical Physics, 2015, Vol 27, Issue 10, p1
- ISSN
0129-055X
- Publication type
Article
- DOI
10.1142/S0129055X15500233