Ill-posedness for one-dimensional wave maps at the critical regularity

Terence Tao

Type: Article

Publication Date: 2000-06-01

Citations: 23

DOI: https://doi.org/10.1353/ajm.2000.0023

Abstract

We show that the wave map equation in R 1+1 is in general ill posed in the critical space Ḣ 1/2 , and the Besov space Ḃ 1/2,1 2 . The problem is attributed to the bad behavior of the one-dimensional bilinear expression D -1 ( fDg ) in these spaces.

Locations

American Journal of Mathematics - View
arXiv (Cornell University) - View - PDF
arXiv (Cornell University) - PDF
American Journal of Mathematics - View
arXiv (Cornell University) - View - PDF
arXiv (Cornell University) - PDF
American Journal of Mathematics - View
arXiv (Cornell University) - View - PDF
arXiv (Cornell University) - PDF

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+	A Priori Estimates and Regularity of Nonlinear Waves	1995	Manoussos G. Grillakis
+	The Cauchy Problem for Harmonic Maps on Minkowski Space	1995	Jalal Shatah
+	On the Regularity of Classical Field Theories in Minkowski Space-Time R3+1	1997	Sergiù Klainerman
+	Weak solutions and development of singularities of the SU(2) σ‐model	1988	Jalal Shatah
+	On the cauchy problem for equivariant wave maps	1994	Jalal Shatah A. Shadi Tahvildar‐Zadeh
+	Smoothing estimates for null forms and applications	1995	Sergiù Klainerman Matei Machedon
+	On the cauchy problem for harmonic maps defined on two-dimensional Minkowski space	1980	Chaohao Gu
+	Remark on the optimal regularity for equations of wave maps type	1997	Sergiù Klainerman Sigmund Selberg
+	Local and global results for wave maps I	1998	Daniel Tataru
+	Unique solvability of the Cauchy problem for the equations of the two-dimensional relativistic chiral fields, taking values in complete Riemann manifolds	1984	O. A. Ladyzhenskaya V.I. Shubov