The local existence and uniqueness of strong solutions for Cauchy problem of three-dimensional inhomogeneous incompressible Navier-Stokes-Vlasov equations

TL;DR

This paper establishes the local existence and uniqueness of strong solutions for the three-dimensional inhomogeneous incompressible Navier-Stokes-Vlasov equations, extending previous results and providing a foundation for further analysis of these complex fluid-kinetic systems.

Contribution

It introduces a linearization and approximation method to prove local existence and uniqueness, enriching the theoretical understanding of Navier-Stokes-Vlasov equations.

Findings

Proves local existence of strong solutions

Establishes uniqueness of solutions

Extends previous existence results for Navier-Stokes-Vlasov systems

Abstract

In this paper, we study the local existence and uniqueness of strong solutions for Cauchy problem of three-dimensional inhomogeneous incompressible Navier-Stokes-Vlasov equations, which are influenced by Young-Pil Choi, Bongsuk Kwon [London Mathematical Society 28 (2015), pp. 3309-3336]\cite{12L}. As for the global well-posedness of the solution of the inhomogeneous incompressible Navier-Stokes-Vlasov equations, this paper first linearizes the inhomogeneous incompressible Navier-Stokes-Vlasov equations, constructs the approximate solution of the linearized equation, and obtains the consistent estimation of the approximate solution. Then, the approximate solution is limited. The local existence and uniqueness of strong solutions for Cauchy problem of inhomogeneous incompressible Navier-Stokes-Vlasov equations are obtained, which further enriches the existence results of strong solutions for Navier-Stokes-Vlasov equations.