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pro vyhledávání: '"Varholm, Kristoffer"'
In this paper, we study two-dimensional traveling waves in finite-depth water that are acted upon solely by gravity. We prove that, for any supercritical Froude number (non-dimensionalized wave speed), there exists a continuous one-parameter family $
Externí odkaz:
http://arxiv.org/abs/2404.08074
We prove exact leading-order asymptotic behaviour at the origin for nontrivial solutions of two families of nonlocal equations. The equations investigated include those satisfied by the cusped highest steady waves for both the uni- and bidirectional
Externí odkaz:
http://arxiv.org/abs/2302.08856
Publikováno v:
Adv. Math. 447 (2024) 109683
We construct small amplitude gravity-capillary water waves with small nonzero vorticity, in three spatial dimensions, bifurcating from uniform flows. The waves are symmetric, and periodic in both horizontal coordinates. The proof is inspired by Lortz
Externí odkaz:
http://arxiv.org/abs/2204.13093
Publikováno v:
In Advances in Mathematics June 2024 447
Autor:
Varholm, Kristoffer
Analytic global bifurcation theory is used to construct a large variety of families of steady periodic two-dimensional gravity water waves with real-analytic vorticity distributions, propagating in an incompressible fluid. The waves that are construc
Externí odkaz:
http://arxiv.org/abs/1907.05736
This paper investigates the stability of traveling wave solutions to the free boundary Euler equations with a submerged point vortex. We prove that sufficiently small-amplitude waves with small enough vortex strength are conditionally orbitally stabl
Externí odkaz:
http://arxiv.org/abs/1811.08024
Akademický článek
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Autor:
Varholm, Kristoffer
We study the mathematical theory of water waves. Local bifurcation theory is also discussed, including the Crandall-Rabinowitz theorem; an abstract theorem used to establish the presence of bifurcation points in the zero set of maps on Banach spaces.
Externí odkaz:
http://urn.kb.se/resolve?urn=urn:nbn:no:ntnu:diva-25748
Autor:
Aasen, Ailo, Varholm, Kristoffer
Publikováno v:
J. Math. Fluid Mech. 20 (2018), no. 1, 161-187
We establish the existence of small-amplitude uni- and bimodal steady periodic gravity waves with an affine vorticity distribution, using a bifurcation argument that differs slightly from earlier theory. The solutions describe waves with critical lay
Externí odkaz:
http://arxiv.org/abs/1508.04664
Autor:
Varholm, Kristoffer
Publikováno v:
Discrete Contin. Dyn. Syst. 36 (2016), no. 7, 3927-3959
We construct small-amplitude solitary traveling gravity-capillary water waves with a finite number of point vortices along a vertical line, on finite depth. This is done using a local bifurcation argument. The properties of the resulting waves are al
Externí odkaz:
http://arxiv.org/abs/1503.06143