Abstract: We discuss results on the global existence and properties (e.g. regularity and uniqueness) of solutions to the Navier-Stokes equations with non-decaying (in a sense), uniformly locally square integrable initial data. Two recent results are examined, including global existence for self-similar and discretely self-similar data as well as initial data in a class containing the critical Morrey spaces. This is joint work with Tai-Peng Tsai.
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