Uniqueness and Decay of Weak Solutions to Phase-Lock Equations - Fan, Jishan; Nakamura, Gen; Zhan, and Mei-Qin (Discontinuity, Nonlinearity, and Complexity, 2026)
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 $(f_0, a_0) \in L^p × L^p$ and $1 < p < 2$ when $d = 1.$ We will also present a result on the decay of $Q$ as time $t→∞.$