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Stratospheric planetary flows from the perspective of the Euler equation on a rotating sphere
Adrian Constantin, Pierre Germain
This article is devoted to stationary solutions of Euler's equation on a rotating sphere, and to their relevance to the dynamics of stratospheric flows in the atmosphere of the out…
Approximations of steady periodic water waves in flows with constant vorticity
Adrian Constantin, Konstantinos Kalimeris, Otmar Scherzer
We provide high-order approximations to periodic travelling wave profiles and to the velocity field and the pressure beneath the waves, in flows with constant vorticity over a flat…
Global bifurcation of steady gravity water waves with critical layers
Adrian Constantin, Walter Strauss, Eugen Varvaruca
We construct large families of two-dimensional travelling water waves propagating under the influence of gravity in a flow of constant vorticity over a flat bed. A Riemann-Hilbert…
Steady periodic water waves with constant vorticity: regularity and local bifurcation
Adrian Constantin, Eugen Varvaruca
This paper studies periodic traveling gravity waves at the free surface of water in a flow of constant vorticity over a flat bed. Using conformal mappings the free-boundary problem…
The hydrodynamical relevance of the Camassa-Holm and Degasperis-Procesi equations
Adrian Constantin, David Lannes
In recent years two nonlinear dispersive partial differential equations have attracted a lot of attention due to their integrable structure. We prove that both equations arise in t…
Global solutions of the Hunter-Saxton equation
Alberto Bressan, Adrian Constantin
We construct a continuous semigroup of weak, dissipative solutions to a nonlinear partial differential equations modeling nematic liquid crystals. A new distance functional, determ…