Uniqueness and Decay of Weak Solutions to Phase-Lock Equations - Fan, Jishan; Nakamura, Gen; Zhan,; 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 L^2 and Q_0 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) 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→∞.