On Agemi-type structural conditions for a system of semilinear wave equations

Abstract

We consider a two-component system of cubic semilinear wave equations in two space dimensions satisfying the Agemi-type structural condition (Ag) but violating (Ag${}_0$) and (Ag${}_{+}$). For this system, we show that small amplitude solutions are asymptotically free as $t\to +\infty$.

arXiv comment16 pages. The title has been changed

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Cited by in corpus (4)

• Large time asymptotics for a cubic nonlinear Schrödinger system in one space dimension
• Global existence for systems of nonlinear wave and Klein-Gordon equations in two space dimensions under a kind of the weak null condition
• Energy decay for small solutions to semilinear wave equations with weakly dissipative structure
• Non-decay of the energy for a system of semilinear wave equations