2023/05/10 by Konstantinos Dareiotis, Benjamin Gess, Dareiotis, Konstantinos +5
Physics and Astronomy · Engineering · Economics, Econometrics and Finance · #Theoretical and Computational Physics #Fluid Dynamics and Thin Films #Stochastic processes and financial applications
paper · pdf · doi:10.48550/arxiv.2305.06017
The stochastic thin-film equation with mobility exponent n∈ [(8)/(3),3) on the one-dimensional torus with multiplicative Stratonovich noise is considered. We show that martingale solutions exist for non-negative initial values. This advances on existing results in three aspects: (1) Non-quadratic mobility with not necessarily strictly positive initial data, (2) Measure-valued initial data, (3) Less spatial regularity of the noise. This is achieved by carrying out a compactness argument based solely on the control of the α-entropy dissipation and the conservation of mass.