Fluid-driven fracture presents an interesting case of crack elasticity and fracture propagation nonlinearly coupled to fluid flow. With the exceptions of a few numerical studies, previous hydraulic fracture modeling efforts have been based on the premise of Linear Elastic Fracture Mechanics (LEFM): specifically, that the damage (aka cohesive) zone associated with the rock breakage near the advancing fracture front is lumped into a singular point, under the tacit assumption that the extent of the cohesive zone is small compared to lengthscales of other physical processes relevant in the HF propagation. The latter include the dissipation in the viscous fluid flow in the fracture channel, of which the fluid lag - a region adjacent to the fracture tip filled with fracturing fluid volatiles and/or infiltrated formation pore fluid - is the extreme manifestation. In this work, we address the validity of the LEFM approach in hydraulic fracturing by considering the solution in the near tip region of a cohesive fracture driven by Newtonian fluid in an impermeable linearelastic rock. First, we show that the solution in general possesses an intricate structure supported by a number of nested lengthscales (a general sentiment for HF), on which different dissipation processes are realized (or are dominant).