Regularity criteria of the three-dimensional MHD system involving one velocity and one vorticity component

Regularity Criteria of the Three-dimensional Mhd System Involving One Velocity and One Vorticity Component

We obtain a regularity criteria of the solution to the three-dimensional magnetohydrodynamics system to remain smooth for all time involving only one velocity and one vorticity component. Moreover, the norm in space and time with which we impose our criteria for the vorticity component is at the scaling invariant level. The proof requires a new decomposition of the four nonlinear terms making u...

One-pot Three-component Synthesis of Phosphonate Derivatives

The stable phosphonate derivatives have easily synthesized by the reactions involving trialkyl(aryl) phosphites and dimethyl acetylenedicarboxylate in the presence of 4-nitrophenol and/or acid chlorides, dialkyl(aryl) phosphites and N-methylimidazole at 70 oC under solventfree conditions.

On the Numerical Solution of One Dimensional Schrodinger Equation with Boundary Conditions Involving Fractional Differential Operators

In this paper we study of collocation method with Radial Basis Function to solve one dimensional time dependent Schrodinger equation in an unbounded domain. To this end, we introduce artificial boundaries and reduce the original problem to an initial boundary value problem in a bounded domain with transparent boundary conditions that involves half order fractional derivative in t. Then in three...

Regularity Criteria for the Generalized MHD Equations

Velocity correlations, diffusion, and stochasticity in a one-dimensional system.

We consider the motion of a test particle in a one-dimensional system of equal-mass point particles. The test particle plays the role of a microscopic "piston" that separates two hard-point gases with different concentrations and arbitrary initial velocity distributions. In the homogeneous case when the gases on either side of the piston are in the same macroscopic state, we compute and analyze...