Improved local well-posedness for quasilinear wave equations in dimension three
From MaRDI portal
Publication:1394583
DOI10.1215/S0012-7094-03-11711-1zbMath1031.35091OpenAlexW2062505370MaRDI QIDQ1394583
Igor Rodnianski, Sergiu Klainerman
Publication date: 7 March 2004
Published in: Duke Mathematical Journal (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1215/s0012-7094-03-11711-1
Second-order nonlinear hyperbolic equations (35L70) Dependence of solutions to PDEs on initial and/or boundary data and/or on parameters of PDEs (35B30) Initial value problems for second-order hyperbolic equations (35L15) Hyperbolic equations on manifolds (58J45)
Related Items (36)
A Local Well-Posedness Result for the Quasilinear Wave Equation in ℝ2+1 ⋮ Free decay of solutions to wave equations on a curved background ⋮ Rough solutions of the Einstein constraints on closed manifolds without near-CMC conditions ⋮ Inverse problems for Lorentzian manifolds and non-linear hyperbolic equations ⋮ Stable shock formation for nearly simple outgoing plane symmetric waves ⋮ A geometric approach for sharp local well-posedness of quasilinear wave equations ⋮ Shock formation for 2\(D\) quasilinear wave systems featuring multiple speeds: blowup for the fastest wave, with non-trivial interactions up to the singularity ⋮ Causal geometry of rough Einstein CMCSH spacetime ⋮ Low regularity solutions for gravity water waves II: the 2D case ⋮ The bounded \(L^2\) curvature conjecture ⋮ Poincaré series of filtration associated with Newton diagram and topological types of singularities ⋮ Sharp local well-posedness for quasilinear wave equations with spherical symmetry ⋮ Dispersive estimates for the Schrödinger equation in a model convex domain and applications ⋮ Nonlinear interaction of three impulsive gravitational waves. II: The wave estimates ⋮ The relativistic Euler equations: remarkable null structures and regularity properties ⋮ Low regularity ill-posedness for elastic waves driven by shock formation ⋮ The relativistic Euler equations: ESI notes on their geo-analytic structures and implications for shocks in 1D and multi-dimensions ⋮ The time-like minimal surface equation in Minkowski space: low regularity solutions ⋮ The hidden null structure of the compressible Euler equations and a prelude to applications ⋮ The resolution of the bounded \(L^2\) curvature conjecture in general relativity ⋮ The resolution of the bounded \(L^2\) curvature conjecture in general relativity ⋮ Rough solutions of Einstein vacuum equations in CMCSH gauge ⋮ Causal geometry of Einstein-vacuum spacetimes with finite curvature flux ⋮ On the geometry of null cones in Einstein-vacuum spacetimes ⋮ Stable ODE-type blowup for some quasilinear wave equations with derivative-quadratic nonlinearities ⋮ A physical space approach to wave equation bilinear estimates ⋮ A priori estimates for solutions to the relativistic Euler equations with a moving vacuum boundary ⋮ Global regularity for the Yang–Mills equations on high dimensional Minkowski space ⋮ Almost optimal local well-posedness for the (3+1)-dimensional Maxwell–Klein–Gordon equations ⋮ Rough sound waves in \(3D\) compressible Euler flow with vorticity ⋮ Rough solutions of the 3-D compressible Euler equations ⋮ A new formulation of the \(3D\) compressible Euler equations with dynamic entropy: remarkable null structures and regularity properties ⋮ Multidimensional nonlinear geometric optics for transport operators with applications to stable shock formation ⋮ Rough solutions of the Einstein vacuum equations ⋮ Global well-posedness for the Maxwell-Klein-Gordon equation in \(4+1\) dimensions: small energy ⋮ Local existence with low regularity for the 2D compressible Euler equations
Cites Work
- Sharp counterexamples for Strichartz estimates for low regularity metrics
- A parametrix construction for wave equations with \(C^{1,1}\) coefficients
- Norm estimates in Besov and Lizorkin-Triebel spaces for the solutions of second-order linear hyperbolic equations
- On Strichartz and eigenfunction estimates for low regularity metrics
- Strichartz estimates for second order hyperbolic operators with nonsmooth coefficients, II
- Strichartz estimates for second order hyperbolic operators with nonsmooth coefficients III
- Local Smoothing of Fourier Integral Operators and Carleson-Sjolin Estimates
- Sobolev and isoperimetric inequalities for riemannian submanifolds
- Local regularity of nonlinear wave equations in three space dimensions
- Counterexamples to Local Existence for Semi-Linear Wave Equations
- Equations d'ondes quasilineaires et estimations de Strichartz
- Newton polygons as lattice points
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
This page was built for publication: Improved local well-posedness for quasilinear wave equations in dimension three