Well-posedness results for a generalized Klein-Gordon-Schrödinger system
Well-posedness results for a generalized Klein-Gordon-Schrödinger system
We consider the Klein-Gordon-Schrödinger system i∂tψ + Δψ = ϕ2ψ − ϕψ, (□ + 1)ϕ = −2|ψ|2ϕ + |ψ|2 with additional cubic terms and Cauchy data ψ(0)=ψ0∈Hs(Rn),ϕ(0)=ϕ0∈Hk(Rn),and (∂tϕ)(0)=ϕ1∈Hk−1(Rn) in space dimensions n = 2 and n = 3. We prove the local existence, uniqueness, and continuous dependence on the data …