On the alpha-Navier-Stokes-Vlasov and the alpha-Navier-Stokes-Vlasov-Fokker-Planck equations

Autor(es)

Pinheiro, Cristyan ^[1] ; Planas, Gabriela ^[1]

Afiliação do(s) autor(es)

^[1] Univ Estadual Campinas, Dept Matemat, Inst Matemat Estat & Comp Cient, Rua Sergio Buarque de Holanda 651, BR-13083859 Campinas, SP - Brazil

• Tipo de documento: Artigo Científico
• Fonte: Journal of Mathematical Physics; v. 62, n. 3 MAR 1 2021.
• Citações Web of Science: 0

Resumo

We consider the alpha -Navier-Stokes equations coupled with a Vlasov type equation to model the flow of an incompressible fluid containing small particles. We prove the existence of global weak solutions to the coupled system subject to periodic boundary conditions. Moreover, we investigate the regularity of weak solutions and the uniqueness of regular solutions. The convergence of its solutions to that of the Navier-Stokes-Vlasov equations when alpha tends to zero is also established. The results are extended to the model with the diffusion of spray, i.e., to the alpha -Navier-Stokes-Vlasov-Fokker-Planck equations. (AU)

• Processo FAPESP: 19/02512-5 - Sistemas e equações diferenciais parciais
• Beneficiário: Marcelo da Silva Montenegro
• Modalidade de apoio: Auxílio à Pesquisa - Temático