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First, a new sufficient condition for uniqueness of weak solutions is provedfor the system of 2D viscous Primitive Equations. Second, global existence anduniqueness are established for several classes of weak solutions with partialinitial regularity, including but not limited to those weak solutions withinitial horizontal regularity, rather than vertical regularity. Our results andanalyses for the problem with phys- ical boundary conditions can be extended tothose with other typical boundary conditions. Most of the results were notavailable before, even for the periodic case.

Uniquenss of Some Weak Solutions for 2D Viscous Primitive Equations