We prove the asymptotic properties of the solutions to the 3D Navier–Stokes system with singular external force, by making use of Fourier localization method, the Littlewood–Paley theory and some subtle estimates in...We prove the asymptotic properties of the solutions to the 3D Navier–Stokes system with singular external force, by making use of Fourier localization method, the Littlewood–Paley theory and some subtle estimates in Fourier–Herz space. The main idea of the proof is motivated by that of Cannone et al. [J. Differential Equations, 314, 316–339(2022)]. We deal either with the nonstationary problem or with the stationary problem where solution may be singular due to singular external force. In this paper, the Fourier–Herz space includes the function space of pseudomeasure type used in Cannone et al. [J. Differential Equations, 314, 316–339(2022)]展开更多
In this paper, we apply Littlewood-Paley theory and Ito integral to get the global existence of stochastic Navier-Stokes equations with Coriolis force in Fourier-Besov spaces. As a comparison, we also give correspondi...In this paper, we apply Littlewood-Paley theory and Ito integral to get the global existence of stochastic Navier-Stokes equations with Coriolis force in Fourier-Besov spaces. As a comparison, we also give corresponding results of the deterministic Navier-Stokes equations with Coriolis force.展开更多
The main purpose of this paper is to derive a new （p,q）-atomic decomposition on the multi-parameter Hardy space HP（X1 × X2） for 0 〈 po 〈 P ≤ 1 for some po and all 1 〈 q 〈 ∞, where X1 ×X2 is the pro...The main purpose of this paper is to derive a new （p,q）-atomic decomposition on the multi-parameter Hardy space HP（X1 × X2） for 0 〈 po 〈 P ≤ 1 for some po and all 1 〈 q 〈 ∞, where X1 ×X2 is the product of two spaces of homogeneous type in the sense of Coifman and Weiss. This decomposition converges in both L^q（X1 × X2） （for 1 〈 q 〈 ∞） and Hardy space HP（X1× X2） （for 0 〈 p _〈 1）. As an application, we prove that an operator T, which is bounded on Lq（X1× X2） for some 1 〈 q 〈 ∞, is bounded from H^p（X1 × X2） to L^p（X1 × X2） if and only if T is bounded uniformly on all （p, q）-product atoms in LP（X1 × X2）. The similar boundedness criterion from HP（X1 × X2） to HP（X1 × X2） is also obtained.展开更多
基金Supported by the National Natural Science Foundation of China (Grant No. 11771423)。
文摘We prove the asymptotic properties of the solutions to the 3D Navier–Stokes system with singular external force, by making use of Fourier localization method, the Littlewood–Paley theory and some subtle estimates in Fourier–Herz space. The main idea of the proof is motivated by that of Cannone et al. [J. Differential Equations, 314, 316–339(2022)]. We deal either with the nonstationary problem or with the stationary problem where solution may be singular due to singular external force. In this paper, the Fourier–Herz space includes the function space of pseudomeasure type used in Cannone et al. [J. Differential Equations, 314, 316–339(2022)]
基金supported by NSFC(Grant Nos.11471309 and 11771423)NSFC of Fujian(Grant No.2017J01564)+1 种基金Teaching Reform Project in Putian University(Grant No.JG201524)supported partly by NSFC(Grant No.11771423)
文摘In this paper, we apply Littlewood-Paley theory and Ito integral to get the global existence of stochastic Navier-Stokes equations with Coriolis force in Fourier-Besov spaces. As a comparison, we also give corresponding results of the deterministic Navier-Stokes equations with Coriolis force.
文摘The main purpose of this paper is to derive a new （p,q）-atomic decomposition on the multi-parameter Hardy space HP（X1 × X2） for 0 〈 po 〈 P ≤ 1 for some po and all 1 〈 q 〈 ∞, where X1 ×X2 is the product of two spaces of homogeneous type in the sense of Coifman and Weiss. This decomposition converges in both L^q（X1 × X2） （for 1 〈 q 〈 ∞） and Hardy space HP（X1× X2） （for 0 〈 p _〈 1）. As an application, we prove that an operator T, which is bounded on Lq（X1× X2） for some 1 〈 q 〈 ∞, is bounded from H^p（X1 × X2） to L^p（X1 × X2） if and only if T is bounded uniformly on all （p, q）-product atoms in LP（X1 × X2）. The similar boundedness criterion from HP（X1 × X2） to HP（X1 × X2） is also obtained.
