Arrest of blow up for the 3D semi-relativistic Schrodinger-Poisson system with pseudo-relativistic diffusion

作者：Abou Salem W^*; Chen T; Vougalter V

来源：Reviews in Mathematical Physics, 2015, 27(10): 1550023.

DOI：10.1142/S0129055X15500233

• Schrodinger-Poisson system
• mean-field dynamics
• pseudo-relativistic diffusion
• fractional Laplacian
• functional spaces
• density matrices
• Cauchy problem
• global existence
• blow up of solutions

We show global well-posedness in energy norm of the semi-relativistic Schrodinger-Poisson system of equations with attractive Coulomb interaction in R-3 in the presence of pseudo-relativistic diffusion. We also discuss sufficient conditions to have well-posedness in L-(lambda) under bar(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.

• 出版日期2015-11
• 单位Saskatoon; Saskatchewan