On the regularity properties of a model problem related to wave maps

1997/04/15 by Sergiu Klainerman, Sergiù Klainerman, Matei Machedon · 76 citations
Engineering · Mathematics · Physics and Astronomy · #Advanced Mathematical Physics Problems #Mathematics #Nonlinear Waves and Solitons #Stability and Controllability of Differential Equations

paper · doi:10.1215/s0012-7094-97-08718-4

published in Duke Mathematical Journal 87(3) (Duke University Press)

openalex publication_date 1997/04/15 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/25

Citations

• Smoothing estimates for null forms and applications
• Space‐time estimates for null forms and the local existence theorem

Cited by

• On the wave equation with quadratic nonlinearities in three space dimensions
• Global regularity of wave maps III. Large energy from \R¹⁺² to hyperbolic spaces
• Endpoint bilinear restriction theorems for the cone, and some sharp null form estimates
• Uniqueness of two-bubble wave maps
• Long time solutions for wave maps with large data
• Nonlocal Cauchy problems for wave equations and applications
• The Cauchy Problem for Wave Maps on a Curved Background
• Some sharp bilinear space-time estimates for the wave equation