Year: 1997
Journal of Partial Differential Equations, Vol. 10 (1997), Iss. 1 : pp. 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.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/1997-JPDE-5579
Journal of Partial Differential Equations, Vol. 10 (1997), Iss. 1 : pp. 19–30
Published online: 1997-01
AMS Subject Headings:
Copyright: COPYRIGHT: © Global Science Press
Pages: 12
Keywords: Wave equation