Finally, k is a scaled physical constant which signifies whether the underlying forcing is attractive, when k <0, or repulsive, when k >0. The hyperbolic-elliptic system (1.1) appears in a variety ofâ€¦ (More)

BACKGROUND
This study examined whether there were associations between individual measures of socio-economic status (SES) and the 12-month prevalence of major depressive disorder (MDD) inâ€¦ (More)

In this paper we prove the global in time regularity for the 2D Boussinesq system with either the zero diffusivity or the zero viscosity. We also prove that as diffusivity(viscosity) goes to zero theâ€¦ (More)

We construct a general type of multivortex solutions of the self-duality equations (the Bogomol'nyi equations) of (2+1) dimensional relativis-tic Chern-Simons model with the non-topological boundaryâ€¦ (More)

We prove that there exists no self-similar finite time blowing up solution to the 3D incompressible Euler equations. The proof uses the vorticity transport formula represented in terms of the back toâ€¦ (More)

In this paper we study 1D equations with nonlocal flux. These models have resemblance of the 2D quasi-geostrophic equation. We show the existence of singularities in finite time and constructâ€¦ (More)

In this paper we study the dynamics of eigenvalues of the deformation tensor for solutions of the 3D incompressible Euler equations. Using the evolution equation of the L2 norm of spectra, we deduceâ€¦ (More)

Weobtain improved regularity criteria for the axisymmetricweak solutions of the three dimensional Navier-Stokes equations with nonzero swirl. In particular we prove that the integrability of singleâ€¦ (More)

This paper establishes several existence and uniqueness results for two families of active scalar equations with velocity fields determined by the scalars through very singular integrals. The firstâ€¦ (More)