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This paper deals with stability and the large-time decay to any given global smooth solutions of the 3D density-dependent incompressible Boussinesq system. The decay rate for solutions of the corresponding Cauchy problem is obtained in this work. With the aid of this decay rate, it is shown that a small perturbation of initial data $(overline{a}_0,overline{theta}_0, overline{u}_0)$ still generates a global smooth solution to the density-dependent Boussinesq system, and this solution keeps close to the reference solution.
In this work, we revisit the study by M. E. Schonbek [11] concerning the problem of existence of global entropic weak solutions for the classical Boussinesq system, as well as the study of the regularity of these solutions by C. J. Amick [1]. We prop
In this paper we prove the almost sure existence of global weak solution to the 3D incompressible Navier-Stokes Equation for a set of large data in $dot{H}^{-alpha}(mathbb{R}^{3})$ or $dot{H}^{-alpha}(mathbb{T}^{3})$ with $0<alphaleq 1/2$. This is ac
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 parabolic interpo
The well-posedness for the supersonic solutions of the Euler-Poisson system for hydrodynamical model in semiconductor devices and plasmas is studied in this paper. We first reformulate the Euler-Poisson system in the supersonic region into a second o
We establish the concept of $alpha$-dissipative solutions for the two-component Hunter-Saxton system under the assumption that either $alpha(x)=1$ or $0leq alpha(x)<1$ for all $xin mathbb{R}$. Furthermore, we investigate the Lipschitz stability of so