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Partial differential equations (PDEs): Existence and uniqueness, regularity, boundary conditions, linear and non-linear operators, stability, soliton theory, integrable PDEs, conservation laws, qualitative dynamics.

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Nondimensionalization of Navier Stokes Equations

The Buckingham-pi theorem says that a dimensional quantity of the form $p = f(p_1, \cdots ,p_k,q_1 \cdots, q_n )$ (where the $p_i$'s dimensions form the fundamental set of units) can be rescaled a …
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