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<p>We study the time-dependent Navier–Stokes system coupled with the heat equation under nonlinear Tresca boundary conditions in two dimension. This frictional slip boundary condition is characterized by a subdifferential property. Employing an effective regularization technique, we reformulate the continuous variational inequality into an equivalent equality problem. We establish the existence and and conditional uniqueness of weak solutions. Furthermore, we develop a fully discrete scheme based on the characteristic method and provide optimal error estimates for velocity, pressure, and temperature. We end the paper with numerical simulation validating the theoretical results.</p>

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Characteristic method for a coupled model of the fluid flow with nonlinear slip boundary conditions

  • 期刊论文

  • 发表日期：

    2026年8月4日

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  • Dania Ati,
  • Rahma Agroum,
  • Mohamed Mbehou,
  • Toni Sayah

摘要

We study the time-dependent Navier–Stokes system coupled with the heat equation under nonlinear Tresca boundary conditions in two dimension. This frictional slip boundary condition is characterized by a subdifferential property. Employing an effective regularization technique, we reformulate the continuous variational inequality into an equivalent equality problem. We establish the existence and and conditional uniqueness of weak solutions. Furthermore, we develop a fully discrete scheme based on the characteristic method and provide optimal error estimates for velocity, pressure, and temperature. We end the paper with numerical simulation validating the theoretical results.