Critical curve for \(p\)-\(q\) systems of nonlinear wave equations in three space dimensions
The Cauchy problem for \(p\)-\(q\) systems of nonlinear wave equations \(u_{tt}-\triangle u=|v|^{p}, v_{tt}-\triangle v=|u|^{q}\) in \(\mathbb{R}^{n}\times [0,+\infty)\) for small initial data is discussed. The authors prove a blow-up theorem for the nonlinearity \((p,q)\) being just on the critical curve in the case \(n=3.\) Moreover, the lower and upper bounds of the lifespan of solutions are precisely estimated, including the subcritical case.
scientific article; zbMATH DE number 1529995
scientific article