Stochastic Landau–Lifshitz–Bloch Equation with Transport Noise: Well-Posedness, Dissipation Enhancement

The Landau–Lifshitz–Bloch equation is the only valid model describing the simulation of heat-assisted magnetic recording around the Curie temperature. In order to explain the noise-induced phenomenon more comprehensively between different equilibrium states, we consider a special type of noise: multiplicative transport noise, to perturb the equation on a torus \({\mathbb {T}}^d, d=2,3\). The existence of martingale weak solution is proved for \(d=2,3\). For \(d=2\), we show the uniqueness, then the strong pathwise solution is established. Compared with other type of Wiener noise, we further show that the transport noise provides the regularizing effect, thus, the energy dissipation is enhanced.