Using the discrete Calderon type reproducing formula and the PlancherelPolya characterization for the Besov and Triebel-Lizorkin spaces, the T1 theorem for the Besov and Triebel-Lizorkin spaces was proved.
Consider the Cauchy problems for an n-dimensional nonlinear system of fluid dynamics equations. The main purpose of this paper is to improve the Fourier splitting method to accomplish the decay estimates with sharp ra...Consider the Cauchy problems for an n-dimensional nonlinear system of fluid dynamics equations. The main purpose of this paper is to improve the Fourier splitting method to accomplish the decay estimates with sharp rates of the global weak solutions of the Cauchy problems. We will couple togeth- er the elementary uniform energy estimates of the global weak solutions and a well known Gronwall＇s inequality to improve the Fourier splitting method. This method was initiated by Maria Schonbek in the 1980＇s to study the op- timal long time asymptotic behaviours of the global weak solutions of the nonlinear system of fluid dynamics equations. As applications, the decay esti- mates with sharp rates of the global weak solutions of the Cauchy problems for n-dimensional incompressible Navier-Stokes equations, for the n-dimensional magnetohydrodynamics equations and for many other very interesting nonlin- ear evolution equations with dissipations can be established.展开更多
In this paper we use the T1 theorem to prove a new characterization with minimum regularity and cancellation conditions for inhomogeneous Besov and Triebel-Lizorkin spaces over spaces of homogeneous type. These result...In this paper we use the T1 theorem to prove a new characterization with minimum regularity and cancellation conditions for inhomogeneous Besov and Triebel-Lizorkin spaces over spaces of homogeneous type. These results are new even for R^n.展开更多
基金One of the authors,DENG Donggao,would like to thank the National Natural Science Foundation of China(Grant No.10171111)the Foundation of Zhongshan University Advanced Research Center for their supports.
文摘Using the discrete Calderon type reproducing formula and the PlancherelPolya characterization for the Besov and Triebel-Lizorkin spaces, the T1 theorem for the Besov and Triebel-Lizorkin spaces was proved.
文摘Consider the Cauchy problems for an n-dimensional nonlinear system of fluid dynamics equations. The main purpose of this paper is to improve the Fourier splitting method to accomplish the decay estimates with sharp rates of the global weak solutions of the Cauchy problems. We will couple togeth- er the elementary uniform energy estimates of the global weak solutions and a well known Gronwall＇s inequality to improve the Fourier splitting method. This method was initiated by Maria Schonbek in the 1980＇s to study the op- timal long time asymptotic behaviours of the global weak solutions of the nonlinear system of fluid dynamics equations. As applications, the decay esti- mates with sharp rates of the global weak solutions of the Cauchy problems for n-dimensional incompressible Navier-Stokes equations, for the n-dimensional magnetohydrodynamics equations and for many other very interesting nonlin- ear evolution equations with dissipations can be established.
基金Supported by National Natural Science Foundation of China (Grant Nos.10726071,10571182)
文摘In this paper we use the T1 theorem to prove a new characterization with minimum regularity and cancellation conditions for inhomogeneous Besov and Triebel-Lizorkin spaces over spaces of homogeneous type. These results are new even for R^n.
