@Article{JPDE-10-19,
author = {},
title = {Remarks on Local Regularity for Two Space Dimensional Wave Maps},
journal = {Journal of Partial Differential Equations},
year = {1997},
volume = {10},
number = {1},
pages = {19--30},
abstract = { In this paper, we continue to study the equation ◻Φ^I+f^I(Φ,∂Φ) = 0 where ◻ = -∂²_t + Δ denotes the standard D' Alembertian in R^{2+1} and the nonlinear terms f have the form f^I = Σ_{JK}Γ^I_{JK}(Φ)Q_0(Φ^J,Φ^K) with Q_0(Φ,φ) = -∂_tΦ∂_tφ + Σ&sup_{i=1}∂_iΦ∂_tφ and Γ^I_{JK} being C^∞ function of Φ. In Y. Zhou [1], we showed that the initial value problem Φ(0,x) = Φ_0(x), ∂_tΦ(0,x) = Φ_1 (x) is locally well posed for Φ_0 ∈ H^{s+1}, Φ_1 ∈ H^s with s = \frac{1}{8}. Here, we shall further prove that the initial value problem is locally well posed for any s > 0.},
issn = {2079-732X},
doi = {https://doi.org/},
url = {http://global-sci.org/intro/article_detail/jpde/5579.html}
}