In this paper we consider the Cauchy problem for a semi-linear system of wave equations with Hamilton structure. We prove the existence of global smooth solution of the system for subcritical case by using conservatio...In this paper we consider the Cauchy problem for a semi-linear system of wave equations with Hamilton structure. We prove the existence of global smooth solution of the system for subcritical case by using conservation of energy and Strichartz＇s estimate. On the basis of Morawetz-Pohozev identity, we obtain the same result for the critical case.展开更多
The purpose of this paper is to study scattering theory for the energy subcritical solutions to the non-radial defocusing inhomogeneous Hartree equation iδ_(t)u+Δu=(I_(a)*|·|^(b)|u|^(p))|·|^(b)|u|^(p-2)u.T...The purpose of this paper is to study scattering theory for the energy subcritical solutions to the non-radial defocusing inhomogeneous Hartree equation iδ_(t)u+Δu=(I_(a)*|·|^(b)|u|^(p))|·|^(b)|u|^(p-2)u.Taking advantage of the decay factor in the nonlinearity instead of the embedding theorem,we establish the scattering criterion for the equation.Together with the Morawetz estimate,we obtain the scattering theory for the energy-subcritical case.展开更多
文摘In this paper we consider the Cauchy problem for a semi-linear system of wave equations with Hamilton structure. We prove the existence of global smooth solution of the system for subcritical case by using conservation of energy and Strichartz＇s estimate. On the basis of Morawetz-Pohozev identity, we obtain the same result for the critical case.
基金supported by Qinghai Natural Science Foundation(No.2024-ZJ-976).
文摘The purpose of this paper is to study scattering theory for the energy subcritical solutions to the non-radial defocusing inhomogeneous Hartree equation iδ_(t)u+Δu=(I_(a)*|·|^(b)|u|^(p))|·|^(b)|u|^(p-2)u.Taking advantage of the decay factor in the nonlinearity instead of the embedding theorem,we establish the scattering criterion for the equation.Together with the Morawetz estimate,we obtain the scattering theory for the energy-subcritical case.
