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

DOI10.1142/S0129055X15500233zbMath1342.82137arXiv1403.3027MaRDI QIDQ5744715

Vitali Vougalter, Thomas Chen, Walid Abou Salem

Publication date: 19 February 2016

Published in: Reviews in Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1403.3027

zbMATH Keywords

density matricesCauchy problemglobal existencefunctional spacesSchrödinger-Poisson systemfractional Laplacianblow-up of solutionsmean-field dynamicspseudo-relativistic diffusion

Mathematics Subject Classification ID

Fractional derivatives and integrals (26A33) NLS equations (nonlinear Schrödinger equations) (35Q55) PDEs in connection with quantum mechanics (35Q40) Quantum dynamics and nonequilibrium statistical mechanics (general) (82C10) Statistical mechanics of plasmas (82D10) Blow-up in context of PDEs (35B44)

Cites Work

• Well-posedness and regularity of generalized Navier-Stokes equations in some critical \(Q\)-spaces
• On the generalized semi-relativistic Schrödinger-Poisson system in \(\mathbb{R}^n\)
• Well-posedness of the Cauchy problem for the fractional power dissipative equations

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