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Slowly Traveling Gravity Waves for Darcy Flow: Existence and Stability of Large Waves

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Abstract

We study surface gravity waves for viscous fluid flows governed by Darcy’s law. The free boundary is acted upon by an external pressure posited to be in traveling wave form with a periodic profile. It has been proven that for any given speed, small external pressures generate small periodic traveling waves that are asymptotically stable. In this work, we construct a class of slowly traveling waves that are of arbitrary size and asymptotically stable. Our results are valid in all dimensions and for both the finite and infinite depth cases.

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Acknowledgements

The authors were partially supported by NSF Grants DMS-2205734 and DMS-2205710. We would like to thank the referees for constructive suggestions.

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  1. Department of Mathematics, University of Maryland, College Park, MD, 20742, USA

    John Brownfield & Huy Q. Nguyen

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  1. John Brownfield
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  2. Huy Q. Nguyen
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Correspondence to Huy Q. Nguyen.

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Communicated by A. Ionescu.

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Brownfield, J., Nguyen, H.Q. Slowly Traveling Gravity Waves for Darcy Flow: Existence and Stability of Large Waves. Commun. Math. Phys. 405, 222 (2024). https://doi.org/10.1007/s00220-024-05103-6

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  • DOI: https://doi.org/10.1007/s00220-024-05103-6

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