# Well-posedness of weak solutions for the time-dependent thermal-fluid-solid multiphysical coupled model

“Well-posedness of weak solutions for the time-dependent thermal-fluid-solid multiphysical coupled model” (2026), by Yi Qin et al. Mathematics research paper. Original abstract below, unchanged. A free PDF is available.

- Authors: Yi Qin, Siyu Yang, Luling Cao, Jian Li
- Published: November 6, 2026
- Field: Mathematics
- DOI: https://doi.org/10.48550/arxiv.2611.09482
- Free PDF: https://arxiv.org/pdf/2611.09482

## Abstract

This paper constructs a time-dependent thermal-fluid-solid multiphysical coupled model describing the interaction between a free fluid and a thermo-poroelastic medium and provides a rigorous mathematical analysis. The model consists of the incompressible Navier-Stokes equations and the heat equation in the free-fluid region, together with the thermo-poroelasticity equations in the porous medium. The two regions are coupled on a fixed interface through conditions for normal velocity, tangential velocity, stress balance, temperature continuity, and heat flux continuity. Under a small-data assumption, we prove the existence and uniqueness of a weak solution for this fully dynamic nonlinear coupled system. The proof employs the Galerkin method to construct semi-discrete approximations, establishes uniform a priori estimates that enable the extension of local solutions to global ones, and invokes compactness arguments to pass to the limit, yielding a solution to the original coupled system.

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