Abstract
AbstractIn this paper we prove a result of almost global existence for some abstract nonlinear PDEs on flat tori and apply it to some concrete equations, namely a nonlinear Schrödinger equation with a convolution potential, a beam equation and a quantum hydrodinamical equation. We also apply it to the stability of plane waves in NLS. The main point is that the abstract result is based on a nonresonance condition much weaker than the usual ones, which rely on the celebrated Bourgain’s Lemma which provides a partition of the “resonant sites” of the Laplace operator on irrational tori.
Funder
European Research Council
PRIN
Publisher
Springer Science and Business Media LLC
Reference47 articles.
1. Bambusi, D.: Birkhoff normal form for some nonlinear PDEs. Commun. Math. Phys. 234, 253–283 (2003)
2. Bambusi, D.: A Birkhoff normal form theorem for some semilinear PDEs. In: Craig, W. (ed.) Hamiltonian Dynamical Systems and Applications. NATO Science for Peace and Security Series, pp. 213–247. Springer, Dordrecht (2008)
3. Bambusi, D.: Asymptotic stability of ground states in some Hamiltonian PDEs with symmetry. Commun. Math. Phys. 320(2), 499–542 (2013)
4. Bambusi, D., Delort, J.-M., Grébert, B., Szeftel, J.: Almost global existence for Hamiltonian semilinear Klein–Gordon equations with small Cauchy data on Zoll manifolds. Commun. Pure Appl. Math. 60(11), 1665–1690 (2007)
5. Bambusi, D., Grébert, B.: Birkhoff normal form for partial differential equations with tame modulus. Duke Math. J. 135(3), 507–567 (2006)
Cited by
2 articles.
订阅此论文施引文献
订阅此论文施引文献,注册后可以免费订阅5篇论文的施引文献,订阅后可以查看论文全部施引文献