O problema de Cauchy para a equação da onda cúbica

Abstract

In this work, we study the result of global well-Posedness for the cubic wave equation @2 t u&#56256;&#56320;_u+u3 = 0 in R_R3, where the Cauchy data is in the Sobolev space Hs(R3)_ Hs&#56256;&#56320;1(R3) with 13 18 < s < 1. The proof is based on the work of T. Roy, [23], in this paper Roy propose a almost conservation law for the energy and from this he get a inequality that together with the local well-posedness theory proved by Lindbald and Sogge in [18] guarantee the global well-posedness for the problem.