Author:
Ai Albert,Ifrim Mihaela,Tataru Daniel
Abstract
AbstractIt has long been conjectured that for nonlinear wave equations that satisfy a nonlinear form of the null condition, the low regularity well-posedness theory can be significantly improved compared to the sharp results of Smith-Tataru for the generic case. The aim of this article is to prove the first result in this direction, namely for the time-like minimal surface equation in the Minkowski space-time. Further, our improvement is substantial, namely by $3/8$
3
/
8
derivatives in two space dimensions and by $1/4$
1
/
4
derivatives in higher dimensions.
Publisher
Springer Science and Business Media LLC
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