共查询到20条相似文献,搜索用时 15 毫秒
1.
Daniel Tataru 《Transactions of the American Mathematical Society》2001,353(2):795-807
The aim of this article is twofold. First we consider the wave equation in the hyperbolic space and obtain the counterparts of the Strichartz type estimates in this context. Next we examine the relationship between semilinear hyperbolic equations in the Minkowski space and in the hyperbolic space. This leads to a simple proof of the recent result of Georgiev, Lindblad and Sogge on global existence for solutions to semilinear hyperbolic problems with small data. Shifting the space-time Strichartz estimates from the hyperbolic space to the Minkowski space yields weighted Strichartz estimates in which extend the ones of Georgiev, Lindblad, and Sogge.
2.
Hatem Mejjaoli 《Journal of Mathematical Analysis and Applications》2008,346(1):41-54
In this paper, we prove dispersive and Strichartz estimates associated for the Dunkl wave equation. 相似文献
3.
Oana Ivanovici 《Mathematische Annalen》2010,347(3):627-673
We consider the wave equation inside a strictly convex domain of dimension 2 and provide counterexamples to optimal Strichartz estimates. Such estimates inside convex domains lose regularity when compared to the flat case (at least for a subset of the usual range of indices), mainly due to microlocal phenomena such as caustics which are generated in arbitrarily small time near the boundary. 相似文献
4.
Vesselin Petkov 《Journal of Functional Analysis》2006,235(2):357-376
We obtain global Strichartz estimates for the solutions u of the wave equation for time-periodic potentials V(t,x) with compact support with respect to x. Our analysis is based on the analytic properties of the cut-off resolvent Rχ(z)=χ(U−1(T)−zI)ψ1, where U(T)=U(T,0) is the monodromy operator and T>0 the period of V(t,x). We show that if Rχ(z) has no poles z∈C, |z|?1, then for n?3, odd, we have a exponential decal of local energy. For n?2, even, we obtain also an uniform decay of local energy assuming that Rχ(z) has no poles z∈C, |z|?1, and Rχ(z) remains bounded for z in a small neighborhood of 0. 相似文献
5.
Matthew D. Blair Hart F. Smith Christopher D. Sogge 《Annales de l'Institut Henri Poincaré (C) Analyse Non Linéaire》2009,26(5):1817-1829
We prove certain mixed-norm Strichartz estimates on manifolds with boundary. Using them we are able to prove new results for the critical and subcritical wave equation in 4-dimensions with Dirichlet or Neumann boundary conditions. We obtain global existence in the subcritical case, as well as global existence for the critical equation with small data. We also can use our Strichartz estimates to prove scattering results for the critical wave equation with Dirichlet boundary conditions in 3-dimensions. 相似文献
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We study the dispersive properties of the linear vibrating plate (LVP) equation. Splitting it into two Schr?dinger-type equations
we show its close relation with the Schr?dinger equation. Then, the homogeneous Sobolev spaces appear to be the natural setting
to show Strichartz-type estimates for the LVP equation. By showing a Kato-Ponce inequality for homogeneous Sobolev spaces,
we prove the well-posedness of the Cauchy problem for the LVP equation with time-dependent potentials. Finally, we exhibit
the sharpness of our results. This is achieved by finding a suitable solution for the stationary homogeneous vibrating plate
equation. 相似文献
9.
Kosuke Ono 《Mathematical Methods in the Applied Sciences》2004,27(16):1843-1863
We study Lp decay estimates of the solution to the Cauchy problem for the dissipative wave equation in even dimensions: (□+?t)u=0 in ?N × (0,∞) for even N=2n?2 with initial data (u,?tu)∣t=0 =(u0,u1). The representation formulas of the solution u(t)=?tS(t)u0 + S(t)(u0+u1) provide the sharp estimates on Lp norms with p?1. Copyright © 2004 John Wiley & Sons, Ltd. 相似文献
10.
Delphine Salort 《Journal of Differential Equations》2007,233(2):543-584
We consider the Liouville equation associated with a metric g of class C2 and we prove dispersion and Strichartz estimates for the solution of this equation in terms of geodesics associated with g. We introduce the notion of focusing and dispersive metric to characterize metrics such that the same dispersion estimate as in the Euclidean case holds. To deal with the case of non-trapped long range perturbation of the Euclidean metric, we prove a global velocity moments effect on the solution. In particular, we obtain global in time Strichartz estimates for metrics such that the dispersion estimate is not satisfied. 相似文献
11.
Delphine Salort 《Comptes Rendus Mathematique》2006,342(7):489-492
We consider the Liouville equation associated to a metric g and we prove dispersion and Strichartz estimates for the solution of this equation in terms of the geometry of the trajectories associated to g. In particular, we obtain global Strichartz estimates in time for metrics where dispersion estimate is false even locally in time. We also study the analogy between Strichartz estimates obtained for the Liouville equation and the Schrödinger equation with variable coefficients. To cite this article: D. Salort, C. R. Acad. Sci. Paris, Ser. I 342 (2006). 相似文献
12.
Jason L. Metcalfe 《Transactions of the American Mathematical Society》2004,356(12):4839-4855
In this paper, we show that certain local Strichartz estimates for solutions of the wave equation exterior to a convex obstacle can be extended to estimates that are global in both space and time. This extends the work that was done previously by H. Smith and C. Sogge in odd spatial dimensions. In order to prove the global estimates, we explore weighted Strichartz estimates for solutions of the wave equation when the Cauchy data and forcing term are compactly supported.
13.
We prove the global-in-time Strichartz estimates for wave equations on the nontrapping asymptotically conic manifolds. We obtain estimates for the full set of wave admissible indices, including the endpoint. The key points are the properties of the microlocalized spectral measure of Laplacian on this setting showed in [18] and a Littlewood–Paley squarefunction estimate. As applications, we prove the global existence and scattering for a family of nonlinear wave equations on this setting. 相似文献
14.
Atanas Stefanov 《Advances in Mathematics》2007,210(1):246-303
We prove global, scale invariant Strichartz estimates for the linear magnetic Schrödinger equation with small time dependent magnetic field. This is done by constructing an appropriate parametrix. As an application, we show a global regularity type result for Schrödinger maps in dimensions n?6. 相似文献
15.
Vittoria Pierfelice 《Mathematische Zeitschrift》2008,260(2):377-392
We prove Strichartz estimates for radial solutions of the Schrödinger and wave equations on Damek–Ricci spaces, and in particular on symmetric spaces of noncompact type and rank one, using the perturbative theory with potentials. The curvature of the noncompact manifold has an influence on the dispersive properties, and indeed we obtain Strichartz estimates with weights at spatial infinity, which are stronger than the standard ones in the flat case. 相似文献
16.
Instead of the L~p estimates,we study the modulation space estimates for the solution to the damped wave equation.Decay properties for both the linear and semilinear equations are obtained.The estimates in modulation space differ in many aspects from those in L~p space. 相似文献
17.
In this paper, Strichartz estimates for the solution of the Schrödinger evolution equation are considered on a mixed normed space with Lorentz norm with respect to the time variable.
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Youngwoo Koh 《Journal of Mathematical Analysis and Applications》2011,373(1):147-160
We study inhomogeneous Strichartz estimates for the Schrödinger equation for dimension n?3. Using a frequency localization, we obtain some improved range of Strichartz estimates for the solution of inhomogeneous Schrödinger equation except dimension n=3. 相似文献
20.
We deal with fixed-time and Strichartz estimates for the Schrödinger propagator as an operator on Wiener amalgam spaces. We discuss the sharpness of the known estimates and we provide some new estimates which generalize the classical ones. As an application, we present a result on the wellposedness of the linear Schrödinger equation with a rough time-dependent potential. 相似文献