This article concerns large time behavior of Ladyzhenskaya model for incompressible viscous flows in ?3. Based on linear L p -L q estimates, the auxiliary decay properties of the solutions and generalized Gronwall typ...This article concerns large time behavior of Ladyzhenskaya model for incompressible viscous flows in ?3. Based on linear L p -L q estimates, the auxiliary decay properties of the solutions and generalized Gronwall type arguments, some optimal upper and lower bounds for the decay of higher order derivatives of solutions are derived without assuming any decay properties of solutions and using Fourier splitting technology.展开更多
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
This paper considers linearized BCL system with viscosity which is firstly derived by J. L. Bona, T. Colin and D. Lannes for the study of motion of water waves. Ldecay estimate is got by means of Fourier analysis and ...This paper considers linearized BCL system with viscosity which is firstly derived by J. L. Bona, T. Colin and D. Lannes for the study of motion of water waves. Ldecay estimate is got by means of Fourier analysis and frequency decomposition. This result plays key role in studying the global well-posedness of corresponding nonlinear system.展开更多
基金the National Natural Science Foundation of China (Grant Nos.10241005,10771001)Natural Science Foundation of Department of Education in Anhui Province (Grant No.KJ2008A025)
文摘This article concerns large time behavior of Ladyzhenskaya model for incompressible viscous flows in ?3. Based on linear L p -L q estimates, the auxiliary decay properties of the solutions and generalized Gronwall type arguments, some optimal upper and lower bounds for the decay of higher order derivatives of solutions are derived without assuming any decay properties of solutions and using Fourier splitting technology.
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(11571092)
文摘This paper considers linearized BCL system with viscosity which is firstly derived by J. L. Bona, T. Colin and D. Lannes for the study of motion of water waves. Ldecay estimate is got by means of Fourier analysis and frequency decomposition. This result plays key role in studying the global well-posedness of corresponding nonlinear system.
