  Most technologically useful materials are polycrystalline microstructures
composed of a myriad of small monocrystalline grains separated by grain
boundaries. The energetics and connectivities of grain boundaries play a
crucial role in defining the main characteristics of materials across a wide
range of scales. In this work, we propose a model for the evolution of the
grain boundary network with dynamic boundary conditions at the triple
junctions, triple junctions drag, and with dynamic lattice misorientations.
Using the energetic variational approach, we derive system of geometric
differential equations to describe motion of such grain boundaries. Next, we
relax curvature effect of the grain boundaries to isolate the effect of the
dynamics of lattice misorientations and triple junctions drag, and we establish
local well-posedness result for the considered model.
