Nonlinear Partial Differential Equations Using Compactness.
Technical summary rept.,
WISCONSIN UNIV MADISON MATHEMATICS RESEARCH CENTER
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After reviewing some general properties of Sobolevs spaces the author gives an abstract framework for Navier-Stokes equations. He examines some technical properties of the functional spaces introduced and proves existence of a solution this is done using Galerkins method and a compactness theorem for the limiting procedure. Uniqueness and regularity properties are proved in dimension 2. Bounded, periodic and stationary solutions are studied as well as stability of small periodic or stationary solutions. The same method is applied to 2 semilinear wave equations. This is done after studying the invariants of the wave equation with application to local decay of energy.
- Theoretical Mathematics
- Fluid Mechanics