English

Slowly traveling gravity waves for Darcy flow: existence and stability of large waves

Analysis of PDEs 2023-12-13 v1 Fluid Dynamics

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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Cite

@article{arxiv.2312.07446,
  title  = {Slowly traveling gravity waves for Darcy flow: existence and stability of large waves},
  author = {John Brownfield and Huy Q. Nguyen},
  journal= {arXiv preprint arXiv:2312.07446},
  year   = {2023}
}

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22 pages