In this article, we consider the global existence and stability issues of the nonlinear Schrödinger equation with partial confinement. First, by establishing some new cross-invariant manifolds and variational problems, a new sharp criterion of global existence is derived in the $ L^{2} $-critical and $ L^{2} $-supercritical cases. Then, the existence of orbitally stable standing waves is obtained in the $ L^{2} $-subcritical and $ L^{2} $-critical cases by taking advantage of the profile decomposition technique. Our work extends and complements some earlier results.
Citation: Min Gong, Hui Jian, Meixia Cai. Sharp criterion of global existence and orbital stability of standing waves for the nonlinear Schrödinger equation with partial confinement[J]. Mathematical Biosciences and Engineering, 2023, 20(10): 18207-18229. doi: 10.3934/mbe.2023809
In this article, we consider the global existence and stability issues of the nonlinear Schrödinger equation with partial confinement. First, by establishing some new cross-invariant manifolds and variational problems, a new sharp criterion of global existence is derived in the $ L^{2} $-critical and $ L^{2} $-supercritical cases. Then, the existence of orbitally stable standing waves is obtained in the $ L^{2} $-subcritical and $ L^{2} $-critical cases by taking advantage of the profile decomposition technique. Our work extends and complements some earlier results.
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Min Gong, Hui Jian, Meixia Cai. Sharp criterion of global existence and orbital stability of standing waves for the nonlinear Schrödinger equation with partial confinement[J]. Mathematical Biosciences and Engineering, 2023, 20(10): 18207-18229. doi: 10.3934/mbe.2023809
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