Global existence of classical solutions to a regularized brine inclusion model

The freezing of salt water leads to phase separation into ice and brine inclusions. The ejection of salt from the ice phase is akin to chemotaxis. We consider a regularization of a free energy for brine inclusions and address its gradient flow on a periodic domain in R-d(d = 2,3). Uniqueness and global existence of classical solutions from initial data in an energy space are established for positive time.

Automated summary

Freezing of salt water leads to separation into ice and brine. The salt ejection from the ice phase resembles chemotaxis. We analyze the gradient flow of a regularized free energy for brine inclusions on a periodic domain in R-d(d = 2,3) and prove uniqueness and global existence of classical solutions from initial data in an energy space for positive time.