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A new approach reveals weak solutions in the Buckley-Leverett system using a compressible model, suggesting applications in fluid dynamics.
This paper proposes a new approach to solving the Buckley-Leverett System, which is to consider a compressible approximation model characterized by a stiff pressure law. Passing to the incompressible limit, the compressible model gives rise to a Hele-Shaw type free boundary limit of Buckley-Leverett System, and it is shown the existence of a weak solution of it.
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Gomes et al. (2026) studied this question.
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