In this paper, we consider the two-dimensional incompressible Navier-Stokes-Landau-Lifshitz system. The first result is the classical Serrin-type blow-up criterion for Navier-Stokes-Landau-Lifshitz system whose index ...In this paper, we consider the two-dimensional incompressible Navier-Stokes-Landau-Lifshitz system. The first result is the classical Serrin-type blow-up criterion for Navier-Stokes-Landau-Lifshitz system whose index is the same as Navier-Stokes equation. More generally, we establish the blow-up criterion in the homogenous Besov space with the negative index whose form is analogue to Serrin-type. As a result, the blow-up criterion in BMO space with respect to spatial variable is also attained. These results can be regarded as the extension of the recent work [Math. Methods Appl. Sci. 46, (2023), 2500–2516].展开更多
In this paper, we introduce the concept of weakly reducible maxi mal triangular algebras S*!which form a large class of maximal t riangular algebras. Let B be a weakly closed algebra containing S, we prove that the co...In this paper, we introduce the concept of weakly reducible maxi mal triangular algebras S*!which form a large class of maximal t riangular algebras. Let B be a weakly closed algebra containing S, we prove that the cohomology spaces Hn(S , B) ( n≥1) are trivial.展开更多
基金supported by The Postgraduate Innovation Project of Guangzhou University(Grant No.JCCX2024-13)supported by the National Natural Science Foundation of China(Grant No.11801107).
文摘In this paper, we consider the two-dimensional incompressible Navier-Stokes-Landau-Lifshitz system. The first result is the classical Serrin-type blow-up criterion for Navier-Stokes-Landau-Lifshitz system whose index is the same as Navier-Stokes equation. More generally, we establish the blow-up criterion in the homogenous Besov space with the negative index whose form is analogue to Serrin-type. As a result, the blow-up criterion in BMO space with respect to spatial variable is also attained. These results can be regarded as the extension of the recent work [Math. Methods Appl. Sci. 46, (2023), 2500–2516].
文摘In this paper, we introduce the concept of weakly reducible maxi mal triangular algebras S*!which form a large class of maximal t riangular algebras. Let B be a weakly closed algebra containing S, we prove that the cohomology spaces Hn(S , B) ( n≥1) are trivial.
基金supported by the National Natural Science Foundation of China(Nos.11271330,11261023,11461033,11401269)the Jiangxi Provincial Natural Science Foundation of China(No.20142BAB201003)
文摘In this paper, some endpoint estimates for the generalized multilinear fractional integrals Ia,m on the non-homogeneous metric spaces are established.
