Tofts, Spencer

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  • Publication
    On the Existence of Solutions to the Muskat Problem With Surface Tension
    (2016-01-01) Tofts, Spencer
    We consider the Muskat Problem with surface tension in two dimensions over the real line, with $H^{s}$ initial data and allowing the two fluids to have different constant densities and viscosities. We take the angle between the interface and the horizontal, and derive an evolution equation for it. We use energy methods to prove that a solution $\theta$ exists locally and can be continued while $