Lower bounds for the life-span of solutions of nonlinear wave equations in three dimensions
AUTOR(ES)
John, Fritz
RESUMO
The paper deals with strict solutions u(x,t) = u(x1,x2,x3,t) of an equation [Formula: see text] where Du is the set of four first derivatives of u. For given initial values u(x,0) = εF(x), ut(x,0) = εG(x), the life span T(ε) is defined as the supremum of all t to which the local solution can be extended for all x. Blowup in finite time corresponds to T(ε) < ∞. Examples show that this can occur for arbitrarily small ε. On the other hand, T(ε) must at least be very large for small ε. By assuming that aik,F,G [unk] C∞, that aik(0) = 0, and that F,G have compact support, it is shown that [Formula: see text] for every N. This result had been established previously only for N < 4.
