Displaying similar documents to “On bilinear estimates for wave equations”

The wave map problem. Small data critical regularity

Igor Rodnianski (2005-2006)

Séminaire Bourbaki


The paper provides a description of the wave map problem with a specific focus on the breakthrough work of T. Tao which showed that a wave map, a dynamic lorentzian analog of a harmonic map, from Minkowski space into a sphere with smooth initial data and a small critical Sobolev norm exists globally in time and remains smooth. When the dimension of the base Minkowski space is ( 2 + 1 ) , the critical norm coincides with energy, the only manifestly conserved quantity in this (lagrangian) theory....

A sharp Strichartz estimate for the wave equation with data in the energy space

Neal Bez, Keith M. Rogers (2013)

Journal of the European Mathematical Society


We prove a sharp bilinear estimate for the wave equation from which we obtain the sharp constant in the Strichartz estimate which controls the L t , x 4 ( 5 + 1 ) norm of the solution in terms of the energy. We also characterise the maximisers.

On bilinear restriction type estimates and applications to nonlinear wave equations

Sergiù Klainerman (1998)

Journées équations aux dérivées partielles


I will start with a short review of the classical restriction theorem for the sphere and Strichartz estimates for the wave equation. I then plan to give a detailed presentation of their recent generalizations in the form of “bilinear estimates”. In addition to the L 2 theory, which is now quite well developed, I plan to discuss a more general point of view concerning the L p theory. By investigating simple examples I will derive necessary conditions for such estimates to be true. I also...

Existence of Global Solutions to Supercritical Semilinear Wave Equations

Georgiev, V. (1996)

Serdica Mathematical Journal


∗The author was partially supported by Alexander von Humboldt Foundation and the Contract MM-516 with the Bulgarian Ministry of Education, Science and Thechnology. In this work we study the existence of global solution to the semilinear wave equation (1.1) (∂2t − ∆)u = F(u), where F(u) = O(|u|^λ) near |u| = 0 and λ > 1. Here and below ∆ denotes the Laplace operator on R^n. The existence of solutions with small initial data, for the case of space dimensions n = 3 was...

Waves of excitations in heterogeneous annular region II. Strong asymmetry

Kristóf Kály-Kullai, András Volford, Henrik Farkas (2003)

Banach Center Publications


Excitation wave propagation in a heterogeneous medium around a circular obstacle is investigated, when the obstacle is located very eccentrically with respect to the interfacial circle separating the slow inner and the fast outer region. Qualitative properties of the permanent wave fronts are described, and the calculated wave forms are presented.