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pro vyhledávání: '"Escher, Joachim"'
It is shown that the two-dimensional Mullins-Sekerka problem is well-posed in all subcritical Sobolev spaces $H^r(\mathbb{R})$ with $r\in(3/2,2).$ This is the first result where this issue is established in an unbounded geometry. The novelty of our a
Externí odkaz:
http://arxiv.org/abs/2308.06083
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 flow is continuously stratified, and the water layer is bounded from be
Externí odkaz:
http://arxiv.org/abs/1911.13046
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-posedness properties for the corresponding Euler-Arnold equations, also c
Externí odkaz:
http://arxiv.org/abs/1911.03238
Autor:
Escher, Joachim, Oldenburg, Reinhard
Publikováno v:
Mitteilungen der DMV; Jun2024, Vol. 32 Issue 2, p112-115, 4p
Akademický článek
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Autor:
Escher, Joachim, Lyons, Tony
Publikováno v:
Journal of Geometric Mechanics, Volume 7, Number 3, 2015, Pages 281--293
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 ensure the existence of temporally global solutions are presented. Moreover
Externí odkaz:
http://arxiv.org/abs/1508.06807
Publikováno v:
Indiana Univ. Math. J., 67(2) (2018), 679-737
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 as surface tension effects. In the absence of surface tension we prove
Externí odkaz:
http://arxiv.org/abs/1507.02601
Publikováno v:
Journal of Differential Equations 258 (Mar 2015), no. 6, 2010-2053
Of concern is the study of fractional order Sobolev--type metrics on the group of $H^{\infty}$-diffeomorphism of $\mathbb{R}^{d}$ and on its Sobolev completions $\mathcal{D}^{q}(\mathbb{R}^{d})$. It is shown that the $H^{s}$-Sobolev metric induces a
Externí odkaz:
http://arxiv.org/abs/1411.4081
Publikováno v:
Annali di Matematica Pura ed Applicata (1923 -) 195 (Feb 2016), no. 1, 249-271
In this paper we derive a two-component system of nonlinear equations which model two-dimensional shallow water waves with constant vorticity. Then we prove well-posedness of this equation using a geometrical framework which allows us to recast this
Externí odkaz:
http://arxiv.org/abs/1406.1645
Lubrication equations for a surfactant-driven flow of a thin layer of fluid are considered with a singular surfactant-dependent surface tension. It is shown that there exists a bounded traveling wave solution which connects a fully surfactant-coated
Externí odkaz:
http://arxiv.org/abs/1401.3300