[PDF] Top 20 Low frequency dispersive estimates for the wave equation in higher dimensions

... proved in [2] for potentials satisfying (1.1) (see also [3], [5]). For higher dimensions Beals [1] proved optimal (without loss of derivatives) dispersive estimates ... Voir le document complet

... perhaps the deepest advantage of the caloric gauge is that it leads to a more favorable nonlinearity than the Coulomb ...precisely, the worst interaction of ψ α in the ... Voir le document complet

... of the solution is localized around a non-dispersive ...heuristically, the degree of homogeneity of the operator works as a threshold for the validity of dispersive ... Voir le document complet

... like the wave one for high frequencies and like the Schr¨ odinger one for low frequencies, and thus we have to establish a dispersive estimate with norm O((1 + |t|) −n/2 ) ... Voir le document complet

... of the solution is localized around a non-dispersive ...heuristically, the degree of homogeneity of the operator works as a threshold for the validity of dispersive ... Voir le document complet

... s−1 in dimension 3 (one can take exactly s = 1/2 in the asymptotically Euclidean case [6], but this is not clear if S 6= S 2 ) but certainly not in higher dimensions (see [6] ... Voir le document complet

... these estimates for h ∈ (0, 1) (high frequency regime) and state similar estimates with h = 1 and χ replaced by χ 0 , localized around 0 (low frequency ...follow the same ... Voir le document complet

... expect estimates like in the Euclidian case: eventually a loss will occur, due to the volume being ...of wave packets may occur as they have nowhere to ...time estimates ... Voir le document complet

... decay estimates for solutions to the wave equation with a poten- tial, ...Vodev, Dispersive estimates of solutions to the wave equation with a ... Voir le document complet

... that the present paper almost repairs an error in [vdH04, Section 5], which was first announced in ...holds for monomial bases. The present “fix” simply consists of converting to ... Voir le document complet

... At the same time, it would be important to repeat the analysis presented in this study on a range of different cli- mate models, although the high-frequency data needed for it is ... Voir le document complet

... [23] Ratner, Marina The central limit theorem for geodesic flows on n-dimensional manifolds of neg- ative curvature. Israel J. Math. 16 (1973), 181–197. [24] Reed, Michael; Simon, Barry Methods of modern ... Voir le document complet

... : in a 2D sim- ulation, each cell of the fluid system is divided into p 0 × p 0 cells for the Helmholtz level, with p 0 = 5 or ...by the CFL criterion for the Euler ... Voir le document complet

... Suppose in addition that H satisfies the finite speed of propagation property, that is the support of the kernel of cos(t √ H) is contained in {(x, y) ∈ X × X, ρ(x, y) ≤ ...proved ... Voir le document complet

... estimate in the L 2 (0, T ; H 1 (Ω)) norm is proposed for the wave ...that the error indi ator η K,1 dened by (12) is sharp even with meshes having large aspe t ...presented ... Voir le document complet

... Abstract. The present paper is dedicated to the proof of dispersive estimates on stratified Lie groups of step 2, for the linear Schr¨ odinger equation involving a ...that ... Voir le document complet

... where the estimates (2.4) and (2.7) hold for s ≥ 0 ...Moreover, the constant C in (2.2) and (2.3) may depend on λ 0 . Proof. The estimate ...proof. The estimates ... Voir le document complet

... to the fact that μ N pointwisely converges to ...theory in (2.3) implies (2.1).  Remark 2.1. Let us point out that the previous reasoning does not allow us to describe the speed of ... Voir le document complet

... all the dispersive effects. Moreover, the KdV and Kawahara equations are known to be well-posed in low indices Sobolev spaces (see for instance [1], [8], [6] ) and one can ask ... Voir le document complet

... OF THE LANDAU EQUATION IN THE COULOMB CASE ...with the large time behaviour of the spatially homogeneous Landau equation with Coulomb ...of the entropy dissipation ... Voir le document complet