Abstract. Soil freeze–thaw processes play a fundamental role in the hydrology, geomorphology, ecology, thermodynamics, and soil chemistry of cold regions' landscapes. In understanding these processes, temperature is used as proxy to represent partitioning ice water content via freezing characteristic curve (SFCC). This mathematical construct relates specific for particular soil. SFCCs depend on...

Abstract The seminal work of DiPerna and Lions (Invent Math 98(3):511–547, 1989) guarantees the existence uniqueness regular Lagrangian flows for Sobolev vector fields. latter is a suitable selection trajectories related ODE satisfying additional compressibility/semigroup properties. A long-standing open question whether flow corollary trajectory a.e. initial datum. Using Ambrosio’s superpositi...