Singularity formation in the incompressible Euler equation in finite and infinite time
TD Drivas, TM Elgindi - EMS Surveys in Mathematical Sciences, 2023 - ems.press
Some classical and recent results on the Euler equations governing perfect (incompressible
and inviscid) fluid motion are collected and reviewed, with some small novelties scattered …
and inviscid) fluid motion are collected and reviewed, with some small novelties scattered …
Existence of non-trivial non-concentrated compactly supported stationary solutions of the 2D Euler equation with finite energy
J Gómez-Serrano, J Park, J Shi - arXiv preprint arXiv:2112.03821, 2021 - arxiv.org
In this paper, we prove the existence of locally non-radial solutions to the stationary 2D Euler
equations with compact support but non-concentrated around one or several points. Our …
equations with compact support but non-concentrated around one or several points. Our …
Existence of Homogeneous Euler Flows of Degree
K Abe - Archive for Rational Mechanics and Analysis, 2024 - Springer
Abstract We consider (-α)-homogeneous solutions to the stationary incompressible Euler
equations in R 3 {0 for α≧ 0 and in R 3 for α< 0. Shvydkoy (2018) demonstrated the …
equations in R 3 {0 for α≧ 0 and in R 3 for α< 0. Shvydkoy (2018) demonstrated the …
The Feynman–Lagerstrom Criterion for Boundary Layers
We study the boundary layer theory for slightly viscous stationary flows forced by an
imposed slip velocity at the boundary. According to the theory of Prandtl (in: International …
imposed slip velocity at the boundary. According to the theory of Prandtl (in: International …
On the distribution of heat in fibered magnetic fields
We study the equilibrium temperature distribution in a model for strongly magnetized
plasmas in dimensions two and three. Provided the magnetic field is sufficiently structured …
plasmas in dimensions two and three. Provided the magnetic field is sufficiently structured …
Islands in stable fluid equilibria
T Drivas, D Ginsberg - Proceedings of the American Mathematical Society, 2024 - ams.org
We prove that stable fluid equilibria with trivial homology on curved, reflection-symmetric
periodic channels must posses “islands”, or cat's eye vortices. In this way, arbitrarily small …
periodic channels must posses “islands”, or cat's eye vortices. In this way, arbitrarily small …
A geometric characterization of steady laminar flow
We study the steady states of the Euler equations on the periodic channel or annulus. We
show that if these flows are laminar (layered by closed non-contractible streamlines which …
show that if these flows are laminar (layered by closed non-contractible streamlines which …
On Two-Dimensional Harmonic Extensions of Vector Fields and Stellarator Coils
AJ Golab, JC Robinson, JL Rodrigo - SIAM Journal on Mathematical Analysis, 2023 - SIAM
We consider a problem relating to magnetic confinement devices known as stellarators.
Plasma is confined by magnetic fields generated by current-carrying coils, and here we …
Plasma is confined by magnetic fields generated by current-carrying coils, and here we …
Existence of homogeneous Euler flows of degree
K Abe - arXiv preprint arXiv:2305.05987, 2023 - arxiv.org
We consider ($-\alpha $)-homogeneous solutions to the stationary incompressible Euler
equations in $\mathbb {R}^{3}\backslash\{0\} $ for $\alpha\geq 0$ and in $\mathbb {R}^{3} …
equations in $\mathbb {R}^{3}\backslash\{0\} $ for $\alpha\geq 0$ and in $\mathbb {R}^{3} …
Stability of Chandrasekhar's nonlinear force-free fields
K Abe - arXiv preprint arXiv:2206.00899, 2022 - arxiv.org
Chandrasekhar's nonlinear force-free field, discovered in 1956, is a rare example of a
nonlinear force-free field describing a large coherent structure of axisymmetric magnetic …
nonlinear force-free field describing a large coherent structure of axisymmetric magnetic …