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
Precise and fast 3D space-charge calculations have become important for high intensity hadron accelerator design. The PIC method is most frequently used due to its efficiency. This paper introduces a 3D-PIC code that ...Precise and fast 3D space-charge calculations have become important for high intensity hadron accelerator design. The PIC method is most frequently used due to its efficiency. This paper introduces a 3D-PIC code that computes the potential of the bunch in the rest frame by means of Poisson＇s equation. FFT is applied as Poisson solvers. The details and the results are presented as well as error analysis.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)]
文摘Precise and fast 3D space-charge calculations have become important for high intensity hadron accelerator design. The PIC method is most frequently used due to its efficiency. This paper introduces a 3D-PIC code that computes the potential of the bunch in the rest frame by means of Poisson＇s equation. FFT is applied as Poisson solvers. The details and the results are presented as well as error analysis.
