Global dynamics below the ground state energy for the Zakharov system in the 3D radial case
Zihua Guo, Kenji Nakanishi, Shuxia Wang
TL;DR
This paper studies the long-term behavior of solutions to the 3D radial Zakharov system when initial energy is below a critical threshold, identifying conditions for scattering or blow-up.
Contribution
It establishes a dichotomy between scattering and grow-up for the Zakharov system below the ground state energy in three dimensions.
Findings
Dichotomy between scattering and grow-up solutions.
Conditions for global existence and blow-up.
Analysis specific to the 3D radial case.
Abstract
We consider the global dynamics below the ground state energy for the Zakharov system in the 3D radial case. We obtain dichotomy between the scattering and the growup.
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Taxonomy
TopicsAdvanced Mathematical Physics Problems · Nonlinear Waves and Solitons · Black Holes and Theoretical Physics