24 citations · 33 across the 13 of their papers we have counts for
8 papers · 2 filters
On the a priori estimates for the Euler, the Navier-Stokes and the quasi-geostrophic equations
Dongho Chae
We prove new \emph{a priori} estimates for the 3D Euler, the 3D Navier-Stokes and the 2D quasi-geostrophic equations by the method of similarity transforms.
On the blow-up problem and new a priori estimates for the 3D Euler and the Navier-Stokes equations
Dongho Chae
We study blow-up rates and the blow-up profiles of possible asymptotically self-similar singularities of the 3D Euler equations, where the sense of convergence and self-similarity…
Global regularity for the 3D Navier-Stokes and the 3D Euler equations
Dongho Chae
The article `Global regularity for the 3D Navier-Stokes and the 3D Euler equations'(arXiv:0711.2453) is withdrawn due to a serious error in the proof.
On the apparition of singularities of vector fields transported by volume preserving diffeomorphisms
Dongho Chae
We consider possible generation of singularities of a vector field transported by diffeomorphisms with derivatives of uniformly bounded determinants. A particular case of volume pr…
Remarks on regularity conditions of the Navier-Stokes equations
Dongho Chae
Let and be the velocity and the vorticity of the a suitable weak solution of the 3D Navier-Stokes equations in a space-time domain containing , and $Q_{z_0…
Nonexistence of self-similar singularities in the viscous magnetohydrodynamics with zero resistivity
Dongho Chae
We are concerned on the possibility of finite time singularity in a partially viscous magnetohydrodynamic equations in , , namely the MHD with positive viscosity a…