## A mathematical introduction to fluid mechanics |

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assume balance of momentum Bernoulli's theorem boundary conditions C_ characteristics called centered rarefaction wave change of variables conservation laws consider constant construction convex defined deflagration denote density derivation determine differential equations differential form discontinuity divergence theorem eigenvalues energy entropy condition Euler Euler's equations example F dx dt family of characteristics fluid mechanics follows force gas dynamics given grad ideal flow incompressible flow incompressible potential flow integral form isentropic Jacobian jump condition kinetic linear mass Math mathematical matrix moving Navier-Stokes equations particle piston path plane potential flow Prandtl equations pressure random variables random walk reaction front region Riemann invariants Riemann problem right centered wave Section l.l separation shown in Figure simple wave simply connected slip line smooth sound speed straight lines streamlines system of conservation theory u-ds unique velocity field vortex line vortex sheets vortex tube vorticity weak solution x-axis zero