65 citations · 457 across the 27 of their papers we have counts for
31 papers · 1 filter
The Mullins-Sekerka problem via the method of potentials
Joachim Escher, Anca-Voichita Matioc, Bogdan-Vasile Matioc
It is shown that the two-dimensional Mullins-Sekerka problem is well-posed in all subcritical Sobolev spaces with This is the first result where th…
Stratified periodic water waves with singular density gradients
Joachim Escher, Patrik Knopf, Christina Lienstromberg +1
We consider Euler's equations for free surface waves traveling on a body of density stratified water in the scenario when gravity and surface tension act as restoring forces. The f…
Well-posedness of the EPDiff equation with a pseudo-differential inertia operator
Martin Bauer, Martins Bruveris, Emanuel Cismas +2
In this article we study the class of right-invariant, fractional order Sobolev-type metrics on groups of diffeomorphisms of a compact manifold M. Our main result concerns well-pos…
Two-component higher order Camassa-Holm systems with fractional inertia operator: a geometric approach
Joachim Escher, Tony Lyons
In the following we study the qualitative properties of solutions to the geodesic flow induced by a higher order two-component Camassa-Holm system. In particular, criteria to ensur…
The domain of parabolicity for the Muskat problem
Joachim Escher, Bogdan-Vasile Matioc, Christoph Walker
We address the well-posedness of the Muskat problem in a periodic geometry and in a setting which allows us to consider general initial and boundary data, gravity effects, as well…
Local and Global Well-posedness of the fractional order EPDiff equation on
Martin Bauer, Joachim Escher, Boris Kolev
Of concern is the study of fractional order Sobolev--type metrics on the group of -diffeomorphism of and on its Sobolev completions $\mathcal{D}^{q}(\m…