Boooooring. Except for Navier-Stokes existence and smoothness. That's OK.
A report on the Navier-Stokes Problem by Vladimir Šverak
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Continuum mechanics is a branch of mechanics that deals with the behavior of materials modeled as continuous mass rather than as discrete particles. It provides a framework for understanding how materials deform and respond to forces when they are subjected to stress, temperature changes, or other influences.