Well-posedness of strong solutions for the Vlasov equation coupled to non-Newtonian fluids in dimension three

2019/01/08 by Kyungkeun Kang, Kang, Kyungkeun, Hwa Kil Kim +3 · 1 citation
Mathematics · #35D35 #35Q30 #35Q83 #76A05 #Analysis of PDEs (math.AP) #FOS: Mathematics #Gas Dynamics and Kinetic Theory #Navier-Stokes equation solutions

paper · pdf · doi:10.48550/arxiv.1901.02162

openalex publication_date 2019/01/08 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We consider the Cauchy problem for coupled system of Vlasov and non-Newtonian fluid equations. We establish local well--posedness of the strong solutions, provided that the initial data are regular enough. Global existence of unique strong solutions for any given time interval is shown as well if the initial data are sufficiently small.

Cited by

• Coupled Vlasov and non-Newtonian fluid dynamics: existence and large-time behavior

Related

• Global weak solutions to the Navier-Stokes-Vlasov equations
• Periodic Vlasov-Stokes' system: Existence and Uniqueness of strong solutions
• Coupled Vlasov and non-Newtonian fluid dynamics: existence and large-time behavior
• Global well-posedness and optimal large-time behavior of strong solutions to the non-isentropic particle-fluid flows
• Global well-posedness for the two dimensional Navier-Stokes-Vlasov Equations