Logarithmic spirals in 2d perfect fluids
We study logarithmic spiraling solutions to the 2d incompressible Euler equations which
solve a nonlinear transport system on $\mathbb {S} $. We show that this system is locally …
solve a nonlinear transport system on $\mathbb {S} $. We show that this system is locally …
Well-posedness of logarithmic spiral vortex sheets
T Cieślak, P Kokocki, WS Ożański - Journal of Differential Equations, 2024 - Elsevier
We consider a family of 2D logarithmic spiral vortex sheets which include the celebrated
spirals introduced by Prandtl (Vorträge aus dem Gebiete der Hydro-und Aerodynamik …
spirals introduced by Prandtl (Vorträge aus dem Gebiete der Hydro-und Aerodynamik …
Existence of nonsymmetric logarithmic spiral vortex sheet solutions to the 2D Euler equations
T Cieślak, P Kokocki, WS Ożański - arXiv preprint arXiv:2207.06056, 2022 - arxiv.org
We consider solutions of the 2D incompressible Euler equation in the form of $ M\geq 1$
cocentric logarithmic spirals. We prove the existence of a generic family of spirals that are …
cocentric logarithmic spirals. We prove the existence of a generic family of spirals that are …
[图书][B] On singular vortex patches, I: Well-posedness issues
The purpose of this work is to discuss the well-posedness theory of singular vortex patches.
Our main results are of two types: well-posedness and ill-posedness. On the well-posedness …
Our main results are of two types: well-posedness and ill-posedness. On the well-posedness …
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 …
On singular vortex patches, I: Well-posedness issues
TM Elgindi, IJ Jeong - arXiv preprint arXiv:1903.00833, 2019 - arxiv.org
The purpose of this work is to discuss the well-posedness theory of singular vortex patches.
Our main results are of two types: well-posedness and ill-posedness. On the well-posedness …
Our main results are of two types: well-posedness and ill-posedness. On the well-posedness …
Linear instability of symmetric logarithmic spiral vortex sheets
T Cieślak, P Kokocki, WS Ożański - Journal of Mathematical Fluid …, 2024 - Springer
We consider Alexander spirals with M≥ 3 branches, that is symmetric logarithmic spiral
vortex sheets. We show that such vortex sheets are linearly unstable in the L∞(Kelvin …
vortex sheets. We show that such vortex sheets are linearly unstable in the L∞(Kelvin …
Stationary self-similar profiles for the two-dimensional inviscid Boussinesq equations
K Abe, D Ginsberg, IJ Jeong - arXiv preprint arXiv:2410.21765, 2024 - arxiv.org
arXiv:2410.21765v1 [math.AP] 29 Oct 2024 Page 1 STATIONARY SELF-SIMILAR PROFILES
FOR THE TWO-DIMENSIONAL INVISCID BOUSSINESQ EQUATIONS KEN ABE, DANIEL …
FOR THE TWO-DIMENSIONAL INVISCID BOUSSINESQ EQUATIONS KEN ABE, DANIEL …
Vortex cusps
VW Elling - Journal of Fluid Mechanics, 2020 - cambridge.org
We consider pairs of self-similar two-dimensional vortex sheets forming cusps, equivalently
single sheets merging into slip condition walls, as in classical Mach reflection at wedges. We …
single sheets merging into slip condition walls, as in classical Mach reflection at wedges. We …
On the winding number for particle trajectories in a disk-like vortex patch of the Euler equations
arXiv:2008.05085v2 [math.AP] 10 Mar 2021 Page 1 arXiv:2008.05085v2 [math.AP] 10 Mar 2021
On the winding number for particle trajectories in a disk-like vortex patch of the Euler equations …
On the winding number for particle trajectories in a disk-like vortex patch of the Euler equations …