on almost global existence for nonrelativistic wave equations in 3d almost global solutions are constructed to three dimensional quadratically nonlinear wave equations the proof relies on generalized energy estimates and a new decay estimate the method applies to equations that are only classically invariant such as the nonlinear system of hyperelasticity 1996 john wiley sons inc

generalized strichartz inequalities for the wave equation strichartz inequalities for the wave equation u f are estimates of the solution u of the cauchy problem for that equation in the form of space time integral norms in terms of similar norms of the inhomogeneity f and of suitable norms of the initial data

global existence of small amplitude solutions to nonlinear klein gordon equations in four space time dimensions consider the following class of nonlinear wave equations square text u u text text f u u u n k g where t 2 1 2 2 2 3 2 is the d alembertian of the 4 dimensional minkowski space time and f a smooth function of u u t x and its first and second partial derivates vanishing together with its first derivatives at u u u 0 in other words f is at least quadratic in u u u in a neighborhood of the trivial solution u 0 we subject u to the pure initial value problem text u mkern 1mu varepsilon text f x u t varepsilon g x at t 0 i v p with f g c 0 3 and e 0 a small parameter

equations d ondes quasilineaires et estimations de strichartz dans cet article notre but est de resoudre des equations d ondes quasilineaires pour des donnees initiales moins regulieres que ce qu imposent les methodes d energie ceci impose de demontrer des estimees de type strichartz pour des operateurs d ondes a coefficients seulement lipschitziens

existence for large times of strict solutions of nonlinear wave equations in three space dimensions for small initial data on considere le probleme aux valeurs initiales pour certaines equations hyperboliques non lineaires d ordre 2

on the number of algebraically independent poincare liapunov constants abstract in this paper an upper bound for the number of algebraically independent poincare liapunov constants in a certain basis for planar polynomial differential systems is given finally it is conjectured that an upper bound for the number of functionally independent poincare liapunov quantities would be m 2 3 m 7 where m is the degree of the polynomial differential system moreover the computational problems which appear in the computation of the poincare liapunov constants and in the determination of the center cases are also discussed

global existence in critical spaces for compressible navier stokes equations we investigate global strong solutions for isentropic compressible fluids with initial data close to a stable equilibrium we obtain the existence and uniqueness of a solution in a functional setting invariant by the scaling of the associated equations more precisely the initial velocity has the same critical regularity index as for the incompressible homogeneous navier stokes equations and one more derivative is needed for the density we point out a smoothing effect on the velocity and a l 1 decay on the difference between the density and the constant reference state the proof lies on uniform estimates for a mixed hyperbolic parabolic linear system with a convection term

percolation for the vacant set of random interlacements we investigate random interlacements on d d 3 this model recently introduced in 8 corresponds to a poisson cloud on the space of doubly infinite trajectories modulo time shift tending to infinity at positive and negative infinite times a nonnegative parameter u measures how many trajectories enter the picture our main interest lies in the percolative properties of the vacant set left by random interlacements at level u we show that for all d 3 the vacant set at level u percolates when u is small this solves an open problem of 8 where this fact has only been established when d 7 it also completes the proof of the nondegeneracy in all dimensions d 3 of the critical parameter u of 8 2008 wiley periodicals inc

uniform decay estimates and the lorentz invariance of the classical wave equation on etudie le comportement asymptotique des solutions de u 0 ou t 2 1 2 n 2 pour des conditions initiales u 0 u t g x en t 0 avec g reguliere a support compact dans r n

existence of global strong solutions in critical spaces for barotropic viscous fluids this paper is dedicated to the study of viscous compressible barotropic fluids in dimension n 2 we address the question of the global existence of strong solutions for initial data close to a constant state having critical besov regularity first this article shows the recent results of charve and danchin arch ration mech anal 198 1 233 271 2010 and chen et al commun pure appl math 63 1173 1224 2010 with a new proof our result relies on a new a priori estimate for the velocity that we derive via the intermediary of the effective velocity which allows us to cancel out the coupling between the density and the velocity as in haspot well posedness in critical spaces for barotropic viscous fluids 2009 second we improve the results of charve and danchin 2010 and chen et al 2010 by adding as in charve and danchin 2010 some regularity on the initial data in low frequencies in this case we obtain global strong solutions for a class of large initial data which rely on the results of hoff arch rational mech anal 139 303 354 1997 hoff commun pure appl math 55 11 1365 1407 2002 and hoff j math fluid mech 7 3 315 338 2005 and those of charve and danchin 2010 and chen et al 2010 we conclude by generalizing these results for general viscosity coefficients

almost global existence to nonlinear wave equations in three space dimensions on considere l existence a t grand de solutions de petite amplitude pour des equations d onde d ordre 2 non lineaires a 4 dimensions d espace temps

sharp local well posedness results for the nonlinear wave equation this article is concerned with local well posedness of the cauchy problem for second order quasilinear hyperbolic equations with rough initial data the new results obtained here are sharp in low dimension

dispersion and strichartz estimates for the liouville equation we consider the liouville equation associated with a metric g of class c2 and we prove dispersion and strichartz estimates for the solution of this equation in terms of geodesics associated with g we introduce the notion of focusing and dispersive metric to characterize metrics such that the same dispersion estimate as in the euclidean case holds to deal with the case of non trapped long range perturbation of the euclidean metric we prove a global velocity moments effect on the solution in particular we obtain global in time strichartz estimates for metrics such that the dispersion estimate is not satisfied