Weak asymptotic methods for 3-D self-gravitating pressureless fluids. Application to the creation and evolution of solar systems from the fully nonlinear Euler-Poisson equations

Autor(es)

Colombeau, M. ^[1]

Afiliação do(s) autor(es)

^[1] Univ Sao Paulo, Inst Matemat & Estatist, Sao Paulo - Brazil

• Tipo de documento: Artigo Científico
• Fonte: Journal of Mathematical Physics; v. 56, n. 6 JUN 2015.
• Citações Web of Science: 5

Resumo

We construct a family of classical continuous functions S(x, y, z, t, epsilon) which tend to satisfy asymptotically the system of selfgravitating pressureless fluids when epsilon -> 0. This produces a weak asymptotic method in the sense of Danilov, Omel'yanov, and Shelkovich. The construction is based on a family of two ordinary differential equations (ODEs) (one for the continuity equation and one for the Euler equation) in classical Banach spaces of continuous functions. This construction applies to 3-D selfgravitating pressureless fluids even in presence of point and string concentrations of matter. The method is constructive which permits to check numerically from standard methods for ODEs that these functions tend to the known or admitted solutions when the latter exist. As a direct application, we present a simulation of formation and evolution of a planetary system from a rotating disk of dust: a theorem in this paper asserts that the observed results are a depiction of functions that satisfy the system with arbitrary precision. (C) 2015 AIP Publishing LLC. (AU)

• Processo FAPESP: 12/15780-9 - Funções Generalizadas e Soluções Irregulares de Equações Lineares e Não-Lineares e Aplicações
• Beneficiário: Mathilde Francoise Charlotte Colombeau-Fonteyne
• Modalidade de apoio: Bolsas no Brasil - Pós-Doutorado