Blowup of small data solutions for a class of quasilinear wave equations in two space dimensions, II
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This article is published in Acta Mathematica.The article was published on 1999-03-01 and is currently open access. It has received 119 citations till now. The article focuses on the topics: Space (mathematics) & Small data.read more
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Existence globale et comportement asymptotique pour l'équation de Klein–Gordon quasi linéaire à données petites en dimension 1
TL;DR: In this paper, a condition necessaire et suffisante sur F sous laquelle the solution devrait exister globalement en temps, pour e assez petit.
Journal ArticleDOI
Equations d'ondes quasilineaires et estimations de strichartz
Hajer Bahouri,Jean-Yves Chemin +1 more
TL;DR: In this paper, notre but est de resoudre des equations d'ondes quasilineaires for des donnees initiales moins regulieres que ce qu'imposent les methodes d'energie.
Journal ArticleDOI
The null condition for quasilinear wave equations in two space dimensions, II
TL;DR: In this paper, a geometric blowup of cusp type was shown to occur at the specified time in two-dimensional quasilinear wave equations with small data of size e, in two space dimensions.
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Shock formation in solutions to the 2D compressible Euler equations in the presence of non-zero vorticity
Jonathan Luk,Jared Speck +1 more
TL;DR: In this paper, the authors studied the Cauchy problem for the compressible Euler equations in two spatial dimensions under any physical barotropic equation of state except that of a Chaplygin gas.
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Global Well‐Posedness of Incompressible Elastodynamics in Two Dimensions
TL;DR: For sufficiently small initial displacements in some weighted Sobolev space, the Cauchy problem of the systems of incompressible isotropic elastodynamics in two space dimensions admits a uniqueness global classical solution as discussed by the authors.
References
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Book
Compressible fluid flow and systems of conservation laws in several space variables
TL;DR: In this paper, the authors describe the ecoulement of chocs as compressible and stabilite, and use it to detect fluides and to compressible choc.
Book
Lectures on Nonlinear Hyperbolic Differential Equations
TL;DR: In this paper, a revised and extended version of well-known lectures by L. Hormander from 1986, four chapters are devoted to weak solutions of systems of conservation laws, and two chapters concern the existence of global solutions or estimates of the lifespan for solutions of nonlinear perturbations of the wave or Klein-Gordon equation with small initial data.
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Uniform decay estimates and the lorentz invariance of the classical wave equation
TL;DR: In this paper, 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.
Book
Blowup for Nonlinear Hyperbolic Equations
TL;DR: The two basic blowup mechanisms are the ODE mechanism and the geometric blowup mechanism as discussed by the authors, which takes place first, and the simultaneous occurrence of the two mechanisms is possible.