منابع مشابه
Greens Functions for the Wave Equation
I gather together known results on fundamental solutions to the wave equation in free space, and Greens functions in tori, boxes, and other domains. From this the corresponding fundamental solutions for the Helmholtz equation are derived, and, for the 2D case the semiclassical approximation interpreted back in the time-domain. Utility: scarring via time-dependent propagation in cavities; Math 4...
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In this article, we consider the compressible Navier-Stokes equation with density dependent viscosity coefficients. We focus on the case where those coefficients vanish on vacuum. We prove the stability of weak solutions for periodic domain Ω = T as well as the whole space Ω = R , when N = 2 and N = 3. The pressure is given by p = ρ , and our result holds for any γ > 1. In particular, we prove ...
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fies the biharmonic equation. The detailed behavior of solutions to the biharmonic equation on regions with corners has been historically difficult to characterize. The problem was first examined by Lord Rayleigh in 1920; in 1973, the existence of infinite oscillations in the domain Green’s function was proven in the case of the right angle by S. Osher. In this paper, we observe that, when the ...
متن کاملExistence & Smoothness of the Navier–stokes Equation
Equation (1) is just Newton’s law f = ma for a fluid element subject to the external force f = (fi(x, t))1 i n and to the forces arising from pressure and friction. Equation (2) just says that the fluid is incompressible. For physically reasonable solutions, we want to make sure u(x, t) does now grow large as |x| → ∞. Hence, we will restrict attention to forces f and initial conditions u◦ that ...
متن کاملStokes and anti-Stokes temporal quantum correlation in Raman Scattering
In this work we study the correlated Stokes and anti-Stokes Raman scattering process, called here SaS. The SaS, proposed by Klyshko in 1977 [1], is an effect where the same phonon participates in the Stokes and anti-Stokes scattering processes. The Feynman diagrams of Figure 1 show the Stokes (S), the anti-Stokes (as) and the SaS processes. The SaS process has not been considered in current tre...
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ژورنال
عنوان ژورنال: Wave Motion
سال: 2015
ISSN: 0165-2125
DOI: 10.1016/j.wavemoti.2015.02.011