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arXiv · 2505.11987

A priori estimates for gaseous flows of Forchheimer-type in heterogeneous porous media

Emine Celik·Luan Hoang·Thinh Kieu
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Abstract

We study isentropic fluid flows of gases of the Forchheimer-type in heterogeneous porous media. The governing equation is a doubly nonlinear parabolic equation with coefficients depending on the spatial variables. Its solutions are subject to a nonlinear Robin boundary condition. We establish the estimates of the solutions for short time in terms of the initial and boundary data. For the proof, the multi-weight versions of the Sobolev inequality, parabolic Sobolev inequality and trace theorem are derived. They are then used to implement the Moser iteration for suitable weighted norms.

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Emine Celik, Luan Hoang, Thinh Kieu. 2025-05-17. A priori estimates for gaseous flows of Forchheimer-type in heterogeneous porous media. https://arxiv.org/abs/2505.11987

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