Équations d'ondes quasilinéaires et estimations de Strichartz

Abstract

Dans cet article, notre but est de résoudre des équations d'ondes quasilinéaires pour des données initiales moins régulières que ce qu'imposent les méthodes d'énergie. Ceci impose de démontrer des estimées de type Strichartz pour des opérateurs d'ondes à coefficients seulement lipschitziens.

Strichartz estimates for second order hyperbolic operators with nonsmooth coefficients III

“…Results in the same direction were independently proved by H. Bahouri and J-Y. Chemin [2], [1] using a different method.…”

Phase Space for the Einstein Equations

“…are obtained in the usual manner, by making a compactly supported variation of the spacetime metric g (4) and once integrating by parts, and are just the (vacuum) Einstein equations. In this respect, the Einstein equations are similar to the equations of motion of most other Lagrangian field theories, such as the classical wave equation.…”

“…where A 1 is linear and A 2 is quadratic in ∂g (4) , and thus the Euler-Lagrange equations are determined by A 2 since compactly supported variations of the divergence terms dA 1 will not contribute to the equations. However, A 2 depends on a choice of frame (cf.…”

Existence of strong solutions for nonisothermal Korteweg system

“…The nonnegative coefficient κ is called the capillarity and may depend on both ρ and T . All the thermodynamic quantities are sum of their classic version (it means independent of w) and of one term in |w| 2 . In this case the free energy F decomposes into a standard part F 0 and an additional term due to gradients of density: The model deriving from a Cahn-Hilliard like free energy (see the pioneering work by J. E. Dunn and J. Serrin in [9] and also in [1,4,10]), the conservation of mass, momentum and energy read: is the intersticial work which is needed in order to ensure the entropy balance and was first introduced by Dunn and Serrin in [9].…”