[PDF] Top 20 Strichartz estimates and the nonlinear Schrödinger-type equations

... than the one studied in [BM16], we can not apply directly the low frequency Littlewood-Paley decomposition given in ...kernel estimates (see Subsection 4.2.1). As a result, we split the low ... Voir le document complet

... Introduction The aim is this paper is twofold. The first one is to generalise Theorem 2 from Burq et all [12] on the global existence of nonlinear Schrödinger equation (NLS) to a ... Voir le document complet

... scale the (gKdV)/(gKP-I) approximation is ...to the (KdV)/(KP-I) limit, we may wonder what is known for the (gKdV)/(gKP-I) asymptotic limit for the travelling ...Concerning the one ... Voir le document complet

... On the one hand, in global dynamic, dispersive properties have been considered in establishing the existence of global (or almost global) solutions for small, localized, smooth data by the works of ... Voir le document complet

... 1 and m = 0, FNLSE reduces to the standard nonlinear Schr¨ odinger equation (NLSE, also known as ...Both the ground states and dynamics properties of NLSE have been extensively studied ... Voir le document complet

... control the largest index by the others. • we use ℓ 1 -type norms to control the Fourier coefficients and the vector fields instead of ℓ 2 -type norms as ...spaces ... Voir le document complet

... in the above theorem seems to be sharp; we refer for example to the survey article [Rob] on the subject of Kato’s smoothing ...effect. The Cauchy problem (1) has been extensively studied in ... Voir le document complet

... (17) The Dirac delta function is omitted here, so ( 17 ) rep- resents the spectrum of the variable part of the solu- ...In the homogeneous case, the spectrum starts with narrow ... Voir le document complet

... dispersive estimates still hold without loss for e it∆ in various situations where the trapped set is hyperbolic and of sufficiently small fractal ...dimension. The influence of the ... Voir le document complet

... since the mid-90’s, the question about whether or not dispersion did hold remained completely open, even for the exterior of a ...time) Strichartz estimates were proved to hold as in R ... Voir le document complet

... between the two frequencies and the Kuznetsov-Ma soliton’s intensity is a periodic ...In the case where the ratio of the above two frequencies are irrational, quasiperiodic ... Voir le document complet

... frequencies and to avoid the problem of resonances. Roughly speaking the nonlinear term generates ...used the same idea to prove that for many random small initial data the ... Voir le document complet

... show the results of Section 2 , if we suppose a suitable asymptotic behavior of the initial value (u(0) ∈ X if α 6 N 4 , u(0) ∈ H 1 (R N ) if α > 4 N ), then we have a sharp lower ...under the ... Voir le document complet

... ] type methods, orbital stability against energy (H 1 loc )-norm perturbations of the same period is known for dnoidal waves [ 2 ], and for snoidal waves [ 13 ] under the additional constraint ... Voir le document complet

... follows the same ideas as that of [KePoVe] or [Bie]. Of course, the general plan is unoriginal : linearization of the non linear equation, then, establishing energy estimates for solutions of ... Voir le document complet

... Altogether, the stated result ...of the exact and time-discrete solutions, an estimate for the local truncation error is obtained by means of Proposi- tion ...to the basic requirement σ ... Voir le document complet

... on the statement of Theorem ...in the case of non necessarily homogeneous nonlinearities satisfying ...compressible type Euler equation, the case of a homogeneous nonlinearity was studied in ... Voir le document complet

... The KdV/KP-I limit of the Nonlinear Schr¨odinger equation ...rigorously the convergence of the amplitude of solutions of Nonlinear-Schr¨odinger type Equations with ... Voir le document complet

... Sharp Strichartz estimates without loss of derivatives were also derived, so that local well- posedness can be deduced for various nonlinear ...problems. The Cauchy theory has been recently ... Voir le document complet

... produce the same type of theorems, provided β induces a Littlewood-Paley ...1.7. Estimates involving angular regularity have been already widely inves- tigated and exploited in the ... Voir le document complet