Lattice study of classical inflaton decay
We study numerically the decay of the inflaton by solving the full nonlinear equations of motion on the lattice. We confirm that parametric resonance is effective in transferring energy from the inflaton to a scalar field as long as the self-interactions of the second field are very small. However, in the very broad resonance case $(q\ensuremath{\gg}1)$ the decay rate is limited by scatterings, which significantly slows down the decay. We also find that the inflaton cannot decay via parametric resonance into a scalar field with moderate self-interactions. This means that the preheating stage may be completely absent in many natural inflationary models.
In this paper, we consider the density-dependent incompressible Navier–Stokes equations in with linearly growing initial velocity at infinity. We obtain a blow-up criterion and global well-posedness of the two-dimensional system. It generalized the local well-posedness results due to the recent work by the first and third authors to the global well-posedness in . Copyright © 2012 John Wiley & Sons, Ltd.