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10 papers · 2 filters
Singularity formation for the incompressible Hall-MHD equations without resistivity
Dongho Chae, Shangkun Weng
In this paper we show that the incompressible Hall-MHD system without resistivity is not globally in time well-posed in any Sobolev space for any $m>\frac{7}{…
Global small solution to the 2D MHD system with a velocity damping term
Jiahong Wu, Yifei Wu, Xiaojing Xu
This paper studies the global well-posedness of the incompressible magnetohydrodynamic (MHD) system with a velocity damping term. We establish the global existence and uniqueness o…
Small global solutions to the damped two-dimensional Boussinesq equations
Dhanapati Adhikari, Chongsheng Cao, Jiahong Wu +1
The two-dimensional (2D) incompressible Euler equations have been thoroughly investigated and the resolution of the global (in time) existence and uniqueness issue is currently in…
Euler's equations and the maximum principle
Dongho Chae
In this paper we use maximum principle in the far field region for the time dependent self-similar Euler equations to exclude discretely self-similar blow-up for the Euler equation…
Liouville-type theorems for the forced Euler equations and the Navier-Stokes equations
Dongho Chae
In this paper we study the Liouville-type properties for solutions to the steady incompressible Euler equations with forces in . If we assume "single signedness condition…
Remarks on the asymptotically discretely self-similar solutions of the Navier-Stokes and the Euler equations
Dongho Chae
We study scenarios of self-similar type blow-up for the incompressible Navier-Stokes and the Euler equations. The previous notions of the discretely (backward) self-similar solutio…