Uniqueness and Decay of Weak Solutions to Phase-Lock Equations
DOI:
https://doi.org/10.5890/DNC.2021.03.003Abstract
In this paper, we prove the uniqueness of weak solutions $(f, Q)$ to the phase-lock equations with $f_0 \in L^2$ and $Q_0 \in L^3$ when the space dimension $d = 3.$ We also prove the uniqueness of weak solutions $(f, a)$ to the Ginzburg-Landau equations with $(f_0, a_0) \in L^p \times L^p$ and $1 < p < 2$ when $d = 1.$ We will also present a result on the decay of $Q$ as time $t\to\infty.$References
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