lecture notes for math 256b version 2019 lenya ryzhik march 14 2019 nothing found here is original except for a few mistakes and misprints here and there these notes are ...
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...Lecture notes for math b version lenya ryzhik march nothing found here is original except a few mistakes and misprints there these are simply record of what i cover in class to spare the students necessity taking readers should consult books better pre sentation context we plan follow following c doering j gibbon applied analysis navier stokes equations majda bertozzi vorticity incompressible flow p constantin foias as well by vladimir sverak on mathematical uid dynamics that can be his website derivation euler equa tions state characterized its density t x velocity u our rst task derive partial dierential govern their evolution they will come from conservation mass newton s second law nally an assumption material properties continuity equation each particle trajectory governed dx dt starting position sometimes called label inverse map back labels if ow suciently smooth forward preserve let us assume constant see deduce preservation neither created nor destroyed case equivalent volume ...