It was proved by Bahouri et al.[9]that the Schrodinger equation on the Heisenberg group H^(d),involving the sublaplacian,is an example of a totally non-dispersive evolution equation:for this reason global dispersive e...It was proved by Bahouri et al.[9]that the Schrodinger equation on the Heisenberg group H^(d),involving the sublaplacian,is an example of a totally non-dispersive evolution equation:for this reason global dispersive estimates cannot hold.This paper aims at establishing local dispersive estimates on H^(d) for the linear Schrodinger equation,by a refined study of the Schrodinger ker-nel St on H^(d).The sharpness of these estimates is discussed through several examples.Our approach,based on the explicit formula of the heat kernel on H^(d) derived by Gaveau[19],is achieved by combining complex analysis and Fourier-Heisenberg tools.As a by-product of our results we establish local Stri-chartz estimates and prove that the kernel St concentrates on quantized hori-zontal hyperplanes of H^(d).展开更多
This paper is concerned with the low Mach number limit for the compressible Navier-Stokes equations in an exterior domain. We present here an approach based on Strichartz estimate defined on a non trapping exterior do...This paper is concerned with the low Mach number limit for the compressible Navier-Stokes equations in an exterior domain. We present here an approach based on Strichartz estimate defined on a non trapping exterior domain and we will be able to show the compactness and strong convergence of the velocity vector field.展开更多
Existing sequential parameter estimation methods use the acoustic pressure of a line array as observations. The modal dispersion curves are employed to estimate the sound speed profile（SSP） and geoacoustic parameter...Existing sequential parameter estimation methods use the acoustic pressure of a line array as observations. The modal dispersion curves are employed to estimate the sound speed profile（SSP） and geoacoustic parameters based on the ensemble Kalman filter. The warping transform is implemented to the signals received by a single hydrophone to obtain the dispersion curves. The experimental data are collected at a range-independent shallow water site in the South China Sea. The results indicate that the SSPs are well estimated and the geoacoustic parameters are also well determined. Comparisons of the observed and estimated modal dispersion curves show good agreement.展开更多
文摘It was proved by Bahouri et al.[9]that the Schrodinger equation on the Heisenberg group H^(d),involving the sublaplacian,is an example of a totally non-dispersive evolution equation:for this reason global dispersive estimates cannot hold.This paper aims at establishing local dispersive estimates on H^(d) for the linear Schrodinger equation,by a refined study of the Schrodinger ker-nel St on H^(d).The sharpness of these estimates is discussed through several examples.Our approach,based on the explicit formula of the heat kernel on H^(d) derived by Gaveau[19],is achieved by combining complex analysis and Fourier-Heisenberg tools.As a by-product of our results we establish local Stri-chartz estimates and prove that the kernel St concentrates on quantized hori-zontal hyperplanes of H^(d).
文摘This paper is concerned with the low Mach number limit for the compressible Navier-Stokes equations in an exterior domain. We present here an approach based on Strichartz estimate defined on a non trapping exterior domain and we will be able to show the compactness and strong convergence of the velocity vector field.
基金Supported by the National Natural Science Foundation of China under Grant Nos 11434012,11774374,11404366 and41561144006
文摘Existing sequential parameter estimation methods use the acoustic pressure of a line array as observations. The modal dispersion curves are employed to estimate the sound speed profile（SSP） and geoacoustic parameters based on the ensemble Kalman filter. The warping transform is implemented to the signals received by a single hydrophone to obtain the dispersion curves. The experimental data are collected at a range-independent shallow water site in the South China Sea. The results indicate that the SSPs are well estimated and the geoacoustic parameters are also well determined. Comparisons of the observed and estimated modal dispersion curves show good agreement.
