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