相关论文: Norm inflation for the Boussinesq system

The early Universe inflation is well known as a promising theory to explain the origin of large scale structure of the Universe, a causal theory for the origin of primordial density fluctuations which may explain the observed density…

In this paper, we study the regularity criteria for the 3D Boussinesq equations in terms of one partial derivative of the velocity in Besov spaces. More precisely, it is proved that if the velocity $u$ holds $\int_{0}^{T}\| \partial_{3}…

We show that a supersymmetric renormalizable theory based on gauge group SO(10) and Higgs system {\bf {10 $\oplus$ 210 $\oplus$ 126 $\oplus$ $\overline{\bf 126}$}} with no scale supergravity can lead to a Starobinsky kind of potential for…

In this paper, we construct a class of global large solution to the compressible Navier-Stokes equations in the whole space $\R^d$. Precisely speaking, our choice of special initial data whose $\dot{B}^{-1}_{\infty,\infty}$ norm can be…

In this article we prove highly improved and flexible Strichartz-type estimates allowing us to generalize the asymptotics we obtained for a stratified and rotating incompressible Navier-Stokes system: for large (and less regular) initial…

The claimed detection of the BICEP2 experiment on the primordial B-mode of cosmic microwave background polarization suggests that cosmic inflation possibly takes place at the energy around the grand unified theory scale given a constraint…

This work is devoted to the well-posedness issue for the low-Mach number limit system obtained from the full compressible Navier-Stokes system, in the whole space. In the case where the initial temperature (or density) is close to a…

We revisit a model of the two-scalar system proposed previously for understanding a small but nonzero cosmological constant. The model provides solutions of the scalar-fields energy $\rho_s$ which behaves truly constant for a limited time…

The asymptotics of the strongly stratified Boussinesq system when the Froude number goes to zero have been previously investigated, but the resulting limit system surprisingly did not depend on the thermal diffusivity $\nu$ ' . In this…

We consider fractional Hartree and cubic nonlinear Schr\"odinger equations on Euclidean space $\mathbb R^d$ and on torus $\mathbb T^d$. We establish norm inflation (a stronger phenomena than standard ill-posedness) at every initial data in…

We are concerned with the long-time solvability for 2D inviscid Boussinesq equations for a larger class of initial data which covers the case of borderline regularity. First we show the local solvability in Besov spaces uniformly with…

In this paper, we first address the space-time decay properties for higher order derivatives of strong solutions to the Boussinesq system in the usual Sobolev space. The decay rates obtained here are optimal. The proof is based on a…

This article proves norm inflation in the critical Sobolev space $H^{3/2}(\mathbb{R})$ for the $b$-Novikov equation, which is a $1$-parameter family of Camassa-Holm-type equations with cubic nonlinearities. This result completes the…

We consider the Cauchy problem to the 3D barotropic compressible Navier-Stokes equation. We prove global well-posedness, assuming that the initial data $(\rho_0-1,u_0)$ has small norms in the critical Besov space…

Little is known about the microscopic physics that gave rise to inflation in our universe. There are many reasons to wonder if the underlying description requires a careful arrangement of ingredients or if inflation was the result of an…

In the context of the $L^\infty$-theory of the 3D NSE, it is shown that suitable smallness of a solution in Besov space $B^{-1}_{\infty, \infty}$ suffices to prevent a possible blow-up.

The phenomenon of stochastic eternal inflation is studied for a chaotic inflation potential in a Bianchi Type I spacetime background. After deriving the appropriate stochastic Klein-Gordon equation, we give details on the conditions for…

A variation of Affleck-Dine mechanism was proposed to generate the observed baryon asymmetry in [1], in which the inflaton was assumed to be a complex scalar field with a weakly broken $U(1)$ symmetry, and the baryon asymmetry generation…

We investigate the circumstances under which cosmic inflation can arise from very inhomogeneous initial conditions using numerical relativity simulations. Previous studies have not considered cases with non-zero momentum density due to…

The most current observational data corroborate the Starobinsky model as one of the strongest candidates in the description of an inflationary regime. Motivated by such success, extensions of the Starobinsky model have been increasingly…