Remark on the optimal regularity for equations of wave maps type

DOI10.1080/03605309708821288zbMath0884.35102OpenAlexW2074084981MaRDI QIDQ4346996

Sigmund Selberg, Sergiu Klainerman

Publication date: 15 April 1998

Published in: Communications in Partial Differential Equations (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1080/03605309708821288

zbMATH Keywords

modified Sobolev-type spacespointwise multiplication properties

Mathematics Subject Classification ID

Related Items (48)

Almost global existence for solution of semilinear klein-gordon equations with small weakly decaying cauchy data ⋮ An asymptotic expansion of two-bubble wave maps in high equivariance classes ⋮ Local existence of energy class solutions for the dirac—klein—gordon equations ⋮ Improved well-posedness for the quadratic derivative nonlinear wave equation in 2D ⋮ BILINEAR ESTIMATES AND APPLICATIONS TO NONLINEAR WAVE EQUATIONS ⋮ Global existence and uniqueness of Schrödinger maps in dimensions \(d\geq 4\) ⋮ Construction of type II blowup solutions for the 1-corotational energy supercritical wave maps ⋮ Global existence and scattering behavior for one dimensional wave maps into Riemannian manifolds ⋮ Concentration compactness for critical radial wave maps ⋮ Global well-posedness for the three dimensional simplified inertial Ericksen-Leslie systems near equilibrium ⋮ Small data wave maps in cyclic spacetime ⋮ Two-bubble dynamics for threshold solutions to the wave maps equation ⋮ Weighted fractional chain rule and nonlinear wave equations with minimal regularity ⋮ Some sharp null-form type estimates for the Klein-Gordon equation ⋮ Uniqueness of <scp>Two‐Bubble</scp> Wave Maps in High Equivariance Classes ⋮ Asymptotic Stability of Harmonic Maps on the Hyperbolic Plane under the Schrödinger Maps Evolution ⋮ Optimal blowup stability for supercritical wave maps ⋮ Sharp local well-posedness for quasilinear wave equations with spherical symmetry ⋮ Global Schrödinger map flows to Kähler manifolds with small data in critical Sobolev spaces: energy critical case ⋮ Asymptotic stability of large energy harmonic maps under the wave map from 2D hyperbolic spaces to 2D hyperbolic spaces ⋮ The wave maps equation and Brownian paths ⋮ Local well-posedness for incompressible neo-Hookean elastic equations in almost critical Sobolev spaces ⋮ Global Schrödinger maps in dimensions \(d\geq 2\): small data in the critical Sobolev spaces ⋮ Global well-posedness for half-wave maps with \(S^2\) and \(\mathbb{H}^2\) targets for small smooth initial data ⋮ Low-regularity Schrödinger maps. II: Global well-posedness in dimensions \(d \geq 3\) ⋮ The Cauchy problem for wave maps on a curved background ⋮ Stable blow up dynamics for the critical co-rotational wave maps and equivariant Yang-Mills problems ⋮ Low regularity solutions for the wave map equation into the 2-D sphere ⋮ Energy dispersed large data wave maps in \(2+1\) dimensions ⋮ On collapse of wave maps ⋮ On the formation of singularities in the critical \(O(3)\) \(\sigma \)-model ⋮ Renormalization and blow-up for wave maps from 𝑆²×ℝ to 𝕊² ⋮ Global well-posedness of hedgehog solutions for the \((3+1)\) Skyrme model ⋮ Uniqueness for critical nonlinear wave equations and wave maps via the energy inequality ⋮ The wave maps equation ⋮ SOME SHARP BILINEAR SPACE–TIME ESTIMATES FOR THE WAVE EQUATION ⋮ LONG TIME SOLUTIONS FOR WAVE MAPS WITH LARGE DATA ⋮ Global regularity of wave maps from \(\mathbb{R}^{2+1}\) to \(H^{2}\). Small energy ⋮ Bilinear space-time estimates for homogeneous wave equations ⋮ On Schrödinger maps ⋮ Local and global results for wave maps I ⋮ On global existence of solutions to nonlinear wave equations of wave map type ⋮ On the optimal local regularity for the Yang-Mills equations in ℝ⁴⁺¹ ⋮ Global well-posedness of the Benjamin–Ono equation in low-regularity spaces ⋮ Absence of self-similar blow-up and local well-posedness for the constant mean-curvature wave equation ⋮ Non-uniqueness of weak solutions to the wave map problem ⋮ Averages over spheres for kinetic transport equations; hyperbolic Sobolev spaces and Strichartz inequalities. ⋮ Stability of stationary wave maps from a curved background to a sphere

Cites Work

• Fourier transform restriction phenomena for certain lattice subsets and applications to nonlinear evolution equations. I: Schrödinger equations
• Smoothing estimates for null forms and applications
• Space‐time estimates for null forms and the local existence theorem

This page was built for publication: Remark on the optimal regularity for equations of wave maps type