7 papers · 1 filter
Global dynamics of a single vortex ring
Dengjun Guo, In-Jee Jeong, Lifeng Zhao
We study the global-in-time dynamics of vortex rings for the three-dimensional incompressible Euler equations, under the assumption of axisymmetric flows without swirl. For a broad…
Homogeneous steady states for the generalized surface quasi-geostrophic equations
Ken Abe, Javier Gómez-Serrano, In-Jee Jeong
We consider homogeneous (stationary self-similar) solutions to the generalized surface quasi-geostrophic (gSQG) equations parametrized by the constant , representing the 2D…
Instantaneous continuous loss of Sobolev regularity for the 3D incompressible Euler equation
In-Jee Jeong, Luis Martínez-Zoroa, Wojciech S. Ożański
We prove instantaneous and continuous-in-time loss of supercritical Sobolev regularity for the 3D incompressible Euler equations in . Namely, for any …
Superlinear gradient growth for 2D Euler equation without boundary
In-Jee Jeong, Yao Yao, Tao Zhou
We consider the vorticity gradient growth of solutions to the two-dimensional Euler equations in domains without boundary, namely in the torus and the whole plane…
Existence and stability of Sadovskii vortices: from patch to smooth vortices
Ken Abe, Kyudong Choi, In-Jee Jeong +2
We establish a scaling-invariant variational framework for steadily translating dipoles of the two-dimensional incompressible Euler equations. Specifically, we consider the maximiz…
MHS equilibria in the non-resistive limit to the randomly forced resistive magnetic relaxation equations
Ken Abe, In-Jee Jeong, Federico Pasqualotto +1
We consider randomly forced resistive magnetic relaxation equations (MRE) with resistivity and a force proportional to on the flat -torus for $…