Search Results - "Misiolek, Gerard"

Geometric Hydrodynamics in Open Problems by Khesin, Boris, Misiołek, Gerard, Shnirelman, Alexander

“…Geometric Hydrodynamics has flourished ever since the celebrated 1966 paper of V. Arnold. In this paper we present a collection of open problems along with…”
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Geometric analysis of the generalized surface quasi-geostrophic equations by Bauer, Martin, Heslin, Patrick, Misiołek, Gerard, Preston, Stephen C.

“…We investigate the geometry of a family of equations in two dimensions which interpolate between the Euler equations of ideal hydrodynamics and the inviscid…”
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Non-Uniform Dependence on Initial Data of Solutions to the Euler Equations of Hydrodynamics by Himonas, A. Alexandrou, Misiołek, Gerard

“…We show that continuous dependence on initial data of solutions to the Euler equations of incompressible hydrodynamics is optimal. More precisely, we prove…”
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On Continuity Properties of Solution Maps of the Generalized SQG Family by Misiołek, Gerard, Vu, Xuan-Truong

“…We study a family of active scalar equations which interpolate between the 2D incompressible Euler equations and the (inviscid) surface quasi-geostrophic…”
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Non-Uniform Dependence for the Periodic CH Equation by Alexandrou Himonas, A., Kenig, Carlos, Misiołek, Gerard

“…We show that the solution map of the periodic CH equation is not uniformly continuous in Sobolev spaces with exponent greater than 3/2. This extends earlier…”
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Geometry of the Madelung Transform by Khesin, Boris, Misiołek, Gerard, Modin, Klas

“…The Madelung transform is known to relate Schrödinger-type equations in quantum mechanics and the Euler equations for barotropic-type fluids. We prove that,…”
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Persistence properties and unique continuation of solutions of the camassa-holm equation by ALEXANDROU HIMONAS, A, MISIOŁEK, Gerard, PONCE, Gustavo, YONG ZHOU

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The Exponential Map of the Group of Area-Preserving Diffeomorphisms of a Surface with Boundary by Benn, James, Misiołek, Gerard, Preston, Stephen C.

“…We prove that the Riemannian exponential map of the right-invariant L 2 metric on the group of volume-preserving diffeomorphisms of a two-dimensional manifold…”
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Axisymmetric Diffeomorphisms and Ideal Fluids on Riemannian 3-Manifolds by Lichtenfelz, Leandro, Misiołek, Gerard, Preston, Stephen C

“…Abstract We study the Riemannian geometry of 3D axisymmetric ideal fluids. We prove that the $L^2$ exponential map on the group of volume-preserving…”
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Conjugate and cut points in ideal fluid motion by Drivas, Theodore D., Misiołek, Gerard, Shi, Bin, Yoneda, Tsuyoshi

“…Two fluid configurations along a flow are conjugate if there is a one parameter family of geodesics (fluid flows) joining them to infinitesimal order…”
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Integrable Evolution Equations on Spaces of Tensor Densities and Their Peakon Solutions by Lenells, Jonatan, Misiołek, Gerard, Tiğlay, Feride

“…We study a family of equations defined on the space of tensor densities of weight λ on the circle and introduce two integrable PDE. One of the equations turns…”
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Generalized Hunter–Saxton equation and the geometry of the group of circle diffeomorphisms by Khesin, Boris, Lenells, Jonatan, Misiołek, Gerard

“…We study an equation lying ‘mid-way’ between the periodic Hunter–Saxton and Camassa–Holm equations, and which describes evolution of rotators in liquid…”
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Fredholm properties of Riemannian exponential maps on diffeomorphism groups by Misiołek, Gerard, Preston, Stephen C.

“…We prove that exponential maps of right-invariant Sobolev H r metrics on a variety of diffeomorphism groups of compact manifolds are nonlinear Fredholm maps of…”
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CONTINUITY OF THE SOLUTION MAP OF THE EULER EQUATIONS IN HÖLDER SPACES AND WEAK NORM INFLATION IN BESOV SPACES by MISIOŁEK, GERARD, YONEDA, TSUYOSHI

“…We construct an example showing that the solution map of the Euler equations is not continuous in the Hölder space from 𝐶¹,𝛼 to L t ∞ C x 1 , α for any 0 <…”
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High-frequency smooth solutions and well-posedness of the Camassa-Holm equation by Himonas, A. Alexandrou, Misiołek, Gerard

“…We construct high-frequency smooth periodic solutions to the Camassa-Holm equation and use them to prove that the related solution map is not uniformly…”
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Euler and Navier–Stokes equations on the hyperbolic plane by Khesin, Boris, Misiołek, Gerard

“…We show that nonuniqueness of the Leray–Hopf solutions of the Navier–Stokes equation on the hyperbolic plane ℍ ² observed by Chan and Czubak is a consequence…”
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Analyticity of the Cauchy problem for an integrable evolution equation by Himonas, A. Alexandrou, Misiolek, Gerard

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The Exponential Map Near Conjugate Points In 2D Hydrodynamics by Misiołek, Gerard

“…We prove that the weak-Riemannian exponential map of the L 2 metric on the group of volume-preserving diffeomorphisms of a compact two-dimensional manifold is…”
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Geometric hydrodynamics via Madelung transform by Khesin, Boris, Misiolek, Gerard, Modin, Klas

“…We introduce a geometric framework to study Newton’s equations on infinite-dimensional configuration spaces of diffeomorphisms and smooth probability…”
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Conjugate points in the Bott-Virasoro group and the KdV equation by Misiolek, Gerard

“…We study the geometry of a right invariant metric on a central extension \widehat{{\cal D}}(S^1) of the diffeomorphism group of a circle (the Bott-Virasoro…”
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