In this paper, upper bounds of the L2-decay rate for the Boussinesq equations are considered. Using the L2 decay rate of solutions for the heat equation, and assuming that the solutions of the Boussinesq equations are...In this paper, upper bounds of the L2-decay rate for the Boussinesq equations are considered. Using the L2 decay rate of solutions for the heat equation, and assuming that the solutions of the Boussinesq equations are smooth, we obtain the upper bounds of L2 decay rate for the smooth solutions and difference between the solutions of the Boussinesq equations and those of the heat system with the same initial data. The decay results may then be obtained by passing to the limit of approximating sequences of solutions. The main tool is the Fourier splitting method.展开更多
The main purpose of this paper is to prove the well-posedness of the two-dimensional Boussinesq equations when the initial vorticity wo C L^1 （R^2） （or the finite Radon measure space）. Using the stream function fo...The main purpose of this paper is to prove the well-posedness of the two-dimensional Boussinesq equations when the initial vorticity wo C L^1 （R^2） （or the finite Radon measure space）. Using the stream function form of the equations and the Schauder fixed-point theorem to get the new proof of these results, we get that when the initial vorticity is smooth, there exists a unique classical solutions for the Cauchy problem of the two dimensional Boussinesq equations.展开更多
文摘In this paper, upper bounds of the L2-decay rate for the Boussinesq equations are considered. Using the L2 decay rate of solutions for the heat equation, and assuming that the solutions of the Boussinesq equations are smooth, we obtain the upper bounds of L2 decay rate for the smooth solutions and difference between the solutions of the Boussinesq equations and those of the heat system with the same initial data. The decay results may then be obtained by passing to the limit of approximating sequences of solutions. The main tool is the Fourier splitting method.
基金supported by the National Natural Science Foundation of China (No. 11171229)supported by 973 program (Grant No. 2011CB711100)
文摘The main purpose of this paper is to prove the well-posedness of the two-dimensional Boussinesq equations when the initial vorticity wo C L^1 （R^2） （or the finite Radon measure space）. Using the stream function form of the equations and the Schauder fixed-point theorem to get the new proof of these results, we get that when the initial vorticity is smooth, there exists a unique classical solutions for the Cauchy problem of the two dimensional Boussinesq equations.
