By means of Fourier frequency localization and Bony＇s paraproduct decomposition, we study the global existence and the uniqueness of the 2D Leray-α Magneta-hydrodynamics model with zero magnetic diffusivity for the ...By means of Fourier frequency localization and Bony＇s paraproduct decomposition, we study the global existence and the uniqueness of the 2D Leray-α Magneta-hydrodynamics model with zero magnetic diffusivity for the general initial data. In view of the profits bring by the α model, then using the energy estimate in the frequency space and the Logarithmic Sobolev inequality, we obtain the estimate ∫0^t ｜｜△u｜｜L∞ds which is crucial to get the global existence for the general initial data.展开更多
We establish the global well-posedness for the multidimensional chemotaxis model with some classes of large initial data,especially the case when the rate of variation of ln v0(v0 is the chemical concentration)contain...We establish the global well-posedness for the multidimensional chemotaxis model with some classes of large initial data,especially the case when the rate of variation of ln v0(v0 is the chemical concentration)contains high oscillation and the initial density near the equilibrium is allowed to have large oscillation in 3D.Besides,we show the optimal time-decay rates of the strong solutions under an additional perturbation assumption,which include specially the situations of d=2,3 and improve the previous time-decay rates.Our method mainly relies on the introduce of the effective velocity and the application of the localization in Fourier spaces.展开更多
文摘By means of Fourier frequency localization and Bony＇s paraproduct decomposition, we study the global existence and the uniqueness of the 2D Leray-α Magneta-hydrodynamics model with zero magnetic diffusivity for the general initial data. In view of the profits bring by the α model, then using the energy estimate in the frequency space and the Logarithmic Sobolev inequality, we obtain the estimate ∫0^t ｜｜△u｜｜L∞ds which is crucial to get the global existence for the general initial data.
基金Supported by the National Natural Science Foundation of China(Grant No.12071043)the National Key Research and Development Program of China(Grant No.2020YFA0712900)。
文摘We establish the global well-posedness for the multidimensional chemotaxis model with some classes of large initial data,especially the case when the rate of variation of ln v0(v0 is the chemical concentration)contains high oscillation and the initial density near the equilibrium is allowed to have large oscillation in 3D.Besides,we show the optimal time-decay rates of the strong solutions under an additional perturbation assumption,which include specially the situations of d=2,3 and improve the previous time-decay rates.Our method mainly relies on the introduce of the effective velocity and the application of the localization in Fourier spaces.
