An approximate treatment of gravitational collapse
Copyright policy )An approximate treatment of gravitational collapse
This work studies a simplified model of the gravitational instability of an initially homogeneous infinite medium, represented by $\TT^d$, based on the approximation that the mean fluid velocity is always proportional to the local acceleration. It is shown that, mathematically, this assumption leads to the restricted Patlak-Keller-Segel model considered by J��ger and Luckhaus or, equivalently, the Smoluchowski equation describing the motion of self-gravitating Brownian particles, coupled to the modified Newtonian potential that is appropriate for an infinite mass distribution. We discuss some of the fundamental properties of a non-local generalization of this model where the effective pressure force is given by a fractional Laplacian with $0
Accepted in Physica D: Nonlinear Phenomena
- Spanish National Research Council Spain
- University of California, San Francisco United States
- Autonomous University of Madrid Spain
- Institute of Mathematical Sciences Spain
Cosmology and Nongalactic Astrophysics (astro-ph.CO), math-ph, FOS: Physical sciences, fractional calculus, PDEs in connection with fluid mechanics, Blow-up in context of PDEs, math.MP, Mathematics - Analysis of PDEs, well-posedness, FOS: Mathematics, PDEs in connection with astronomy and astrophysics, Galactic and stellar dynamics, Instrumentation and Methods for Astrophysics (astro-ph.IM), math.AP, Mathematical Physics, instant analyticity, Mathematical Physics (math-ph), Patlak-Keller-Segel model, astro-ph.CO, Dependence of solutions to PDEs on initial and/or boundary data and/or on parameters of PDEs, gravitational collapse, Astrophysics - Instrumentation and Methods for Astrophysics, blow-up, astro-ph.IM, Mixed-type systems of PDEs, Astrophysics - Cosmology and Nongalactic Astrophysics, Analysis of PDEs (math.AP)
Cosmology and Nongalactic Astrophysics (astro-ph.CO), math-ph, FOS: Physical sciences, fractional calculus, PDEs in connection with fluid mechanics, Blow-up in context of PDEs, math.MP, Mathematics - Analysis of PDEs, well-posedness, FOS: Mathematics, PDEs in connection with astronomy and astrophysics, Galactic and stellar dynamics, Instrumentation and Methods for Astrophysics (astro-ph.IM), math.AP, Mathematical Physics, instant analyticity, Mathematical Physics (math-ph), Patlak-Keller-Segel model, astro-ph.CO, Dependence of solutions to PDEs on initial and/or boundary data and/or on parameters of PDEs, gravitational collapse, Astrophysics - Instrumentation and Methods for Astrophysics, blow-up, astro-ph.IM, Mixed-type systems of PDEs, Astrophysics - Cosmology and Nongalactic Astrophysics, Analysis of PDEs (math.AP)
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