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Article Dans Une Revue Communications in Mathematical Sciences Année : 2022

Lake equations with an evanescent or emergent island

Lars Eric Hientzsch
Christophe Lacave
Evelyne Miot

Résumé

We study the asymptotic dynamics of the lake equations in the following two cases, an island shrinking to a point and an emerging island. For both cases, we derive an asymptotic lake-type equation. In the former case, the asymptotic dynamics includes an additional Dirac mass in the vorticity. The main mathematical difficulty is that the equations are singular when the water depth vanishes. We provide new uniform estimates in weighted spaces for the related stream functions which will imply the compactness result.
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Dates et versions

hal-03189403 , version 1 (03-04-2021)
hal-03189403 , version 2 (03-06-2021)

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Lars Eric Hientzsch, Christophe Lacave, Evelyne Miot. Lake equations with an evanescent or emergent island. Communications in Mathematical Sciences, 2022, 20 (1), pp.85 - 122. ⟨10.4310/CMS.2022.v20.n1.a3⟩. ⟨hal-03189403v2⟩
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