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We consider a flow of heat conducting compressible fluid inside a moving domain whose shape in time is prescribed. The flow is governed by the 3-D Navier-Stokes-Fourier system where the velocity is supposed to fulfil the full-slip boundary condition and the temperature on the boundary is given by a nonhomogeneous Dirichlet condition. We establish the global-in-time weak solution to the system, and the approach is based on the penalization of the boundary behavior, viscosity and the pressure in the weak formulation. Moreover, to accommodate the nonhomogeneous boundary heat flux, we introduce the concept of ballistic energy in this work.

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On the Motion of a Heat Conducting Compressible Fluid in Moving Domain with Nonhomogeneous Boundary

  • 会议论文

  • 发表日期：

    2025年

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  • Kuntal Bhandari,
  • Šárka Nečasová

摘要

We consider a flow of heat conducting compressible fluid inside a moving domain whose shape in time is prescribed. The flow is governed by the 3-D Navier-Stokes-Fourier system where the velocity is supposed to fulfil the full-slip boundary condition and the temperature on the boundary is given by a nonhomogeneous Dirichlet condition. We establish the global-in-time weak solution to the system, and the approach is based on the penalization of the boundary behavior, viscosity and the pressure in the weak formulation. Moreover, to accommodate the nonhomogeneous boundary heat flux, we introduce the concept of ballistic energy in this work.