This is a follow-up of our recent article Deng et al. (2004). In Deng et al. (2004), we derive some local geometric conditions on vortex filaments which can prevent finite time blowup of the 3D incompressible Euler equation. In this article, we derive improved geometric conditions which can be applied to the scenario when velocity blows up at the same time… (More)
By exploring a local geometric property of the vorticity field along a vortex filament, we establish a sharp relationship between the geometric properties of the vorticity field and the maximum vortex stretching. This new understanding leads to an improved result of the global existence of the 3D Euler equation under mild assumptions.
In this article we apply the technique proposed in Deng-Hou-Yu  to study the level set dynamics of the 2D quasi-geostrophic equation. Under certain assumptions on the local geometric regularity of the level sets of θ, we obtain global regularity results with improved growth estimate on ∇ ⊥ θ. We further perform numerical simulations to study the local… (More)
A natural condition on the structure of the underlying chemical reaction network, namely weak reversibility, is shown to guarantee the existence of an equilibrium (steady state) in each positive stoichiometric compatibility class for the associated mass-action system. Furthermore, an index formula is given for the set of equilibria in a given stoichiometric… (More)
We explore a level set representation of vorticity in the study of the singularity problems for incompressible fluid models. This representation exists for all initial vorticity fields. We further apply it to study the 3D Lagrangian averaged Euler equations and the 3D Euler equations, and obtain new global existence conditions.
a conjecture on the dimension of the bivariate spline space S r 2r () over the Morgan–Scott triangulation was posed. In this paper, it is proved that the conjecture should be modified for all even r > 2.
Lunar obstacle detection is the key technique for Lunar lander landing, the main step to detect obstacles is to separate and extract the obstacle regions. This paper puts forward a watershed method based on multi-scale mathematical morphology operation to separate the obstacles of the lunar. The method put up multi-scale open and close operator to… (More)