94 citations · 255 across the 23 of their papers we have counts for
11 papers · 1 filter
Distance Geometry and a Hydrodynamical Hopf-Rinow Criterion
Theodore D. Drivas, Patrick Heslin, Gerard Misiołek
The hydrodynamical Hopf-Rinow problem asks whether a given reconfiguration of an ideal fluid can be attained by an Euler flow. On the flat two-dimensional torus, we give an equival…
Regularity of solution maps of the generalized surface quasi-geostrophic equations
Gerard Misiołek, Xuan-Truong Vu, Tsuyoshi Yoneda
We study regularity properties of the data-to-solution maps of the family of generalized surface quasi-geostrophic equations which includes both the 2D incompressible Euler and the…
Conjugate and cut points in ideal fluid motion
Theodore D. Drivas, Gerard Misiołek, Bin Shi +1
Two fluid configurations along a flow are conjugate if there is a one parameter family of geodesics (fluid flows) joining them to infinitesimal order. Geometrically, they can be se…
Continuity of the solution map of the Euler equations in Hölder spaces and weak norm inflation in Besov spaces
Gerard Misiołek, Tsuyoshi Yoneda
We construct an example showing that the solution map of the Euler equations is not continuous in the Hölder space from to for any . On the o…
Loss of continuity of the solution map for the Euler equations in -modulation and Hölder spaces
Gerard Misiołek, Tsuyoshi Yoneda
We study the incompressible Euler equations in the -modulation and Hölder spaces on the plane. We show that for these spaces the associated data-to-sol…
Local ill-posedness of the Euler equations in
Gerard Misiołek, Tsuyoshi Yoneda
We show that the incompressible Euler equations on are not locally well-posed in the sense of Hadamard in the Besov space . Our approach relies on th…
Ill-posedness of the incompressible Euler equations in the space
Gerard Misiołek, Tsuyoshi Yoneda
We prove that the 2D Euler equations are not locally well-posed in . Our approach relies on the technique of Lagrangian deformations and norm inflation of Bourgain and Li. We…
The Euler and Navier-Stokes equations on the hyperbolic plane
Boris Khesin, Gerard Misiolek
We show that non-uniqueness of the Leray-Hopf solutions of the Navier--Stokes equation on the hyperbolic plane observed in arXiv:1006.2819 is a consequence of the Hodge decompositi…
Curvatures of Sobolev metrics on diffeomorphism groups
Boris Khesin, Jonatan Lenells, Gerard Misiolek +1
Many conservative partial differential equations correspond to geodesic equations on groups of diffeomorphisms. Stability of their solutions can be studied by examining sectional c…
Integrable evolution equations on spaces of tensor densities and their peakon solutions
Jonatan Lenells, Gerard Misiołek, Feride Tiğlay
We study a family of equations defined on the space of tensor densities of weight on the circle and introduce two integrable PDE. One of the equations turns out to be closely r…
Persistence Properties and Unique Continuation of solutions of the Camassa-Holm equation
A. Alexandrou Himonas, Gerard Misiołek, Gustavo Ponce +1
It is shown that a strong solution of the Camassa-Holm equation, initially decaying exponentially together with its spacial derivative, must be identically equal to zero if it also…