Teoria de Littlewood-Paley e o problema de Cauchy para a equação da onda cúbica
Abstract
In this work, we study the result of well-posedness for the cubic wave equation
u + u3 = 0 in R3, due to H. Bahouri e J.-Y. Chemin, where the Cauchy data is in
the Homogeneous Sobolev space ̇H3/4(R3) × ̇H−1/4(R3). The proof relies on nonlinear in-
terpolation method, the Bony's decomposition and the logarithmic Strichartz estimates,
as formulated in the Littlewood-Paley Theory