ar X iv : 0 90 1 . 00 22 v 4 [ m at h . A P ] 2 5 O ct 2 01 0 CONCERNING THE WAVE EQUATION ON ASYMPTOTICALLY EUCLIDEAN
نویسنده
چکیده
We obtain KSS, Strichartz and certain weighted Strichartz estimates for the wave equation on (R, g), d ≥ 3, when metric g is non-trapping and approaches the Euclidean metric like 〈x〉 with ρ > 0. Using the KSS estimate, we prove almost global existence for quadratically semilinear wave equations with small initial data for ρ > 1 and d = 3. Also, we establish the Strauss conjecture when the metric is radial with ρ > 0 for d = 3.
منابع مشابه
ar X iv : 0 71 0 . 27 28 v 1 [ m at h . N T ] 1 5 O ct 2 00 7 PRIMES IN TUPLES II
We prove that lim inf n→∞ pn+1 − pn √ log pn(log log pn) < ∞, where pn denotes the n prime. Since on average pn+1 −pn is asymptotically log pn, this shows that we can always find pairs of primes much closer together than the average. We actually prove a more general result concerning the set of values taken on by the differences p− p between primes which includes the small gap result above.
متن کاملar X iv : h ep - p h / 02 10 07 4 v 1 4 O ct 2 00 2 Effective vertex for π 0 γγ §
The π 0 γγ vertex is used as an explicit example of the subtleties connected with the application of equation of motion within Chiral Perturbation Theory at the order O(p 6).
متن کاملar X iv : q ua nt - p h / 01 10 10 4 v 1 1 7 O ct 2 00 1 Superoscillations and tunneling times
It is proposed that superoscillations play an important role in the interferences which give rise to superluminal effects. To exemplify that, we consider a toy model which allows for a wave packet to travel, in zero time and negligible distortion a distance arbitrarily larger than the width of the wave packet. The peak is shown to result from a superoscillatory superposition at the tail. Simila...
متن کاملar X iv : m at h - ph / 0 40 90 62 v 2 1 3 O ct 2 00 4 A remark on rational isochronous potentials
We consider the rational potentials of the one-dimensional mechanical systems, which have a family of periodic solutions with the same period (isochronous potentials). We prove that up to a shift and adding a constant all such potentials have the form U (x) = 1 2 ω 2 x 2 or U (x) = 1 8 ω 2 x 2 + c 2 x −2 .
متن کامل