The generalized Burgers' equation and the Navier-Stokes equation in with singular initial data

Author:
Joel D. Avrin

Journal:
Proc. Amer. Math. Soc. **101** (1987), 29-40

MSC:
Primary 35Q10; Secondary 35K55, 35Q20

MathSciNet review:
897066

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Abstract: From an abstract theory of Weissler we construct a simple local existence theory for a generalization of Burgers' equation and the Navier-Stokes equation in the Banach space . Our conditions on recover the conditions of Giga and Weissler in the latter case except for the borderline situation . For the generalized Burgers' equation our results are apparently new; moreover we show that these local solutions are in fact global solutions in this case. We also obtain results for the generalized Burgers' equation with replaced by a bounded domain with smooth boundary. Using a somewhat more complex abstract theory of Weissler, we are able to improve on our results found in the case , and also obtain global existence.

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DOI:
https://doi.org/10.1090/S0002-9939-1987-0897066-5

Article copyright:
© Copyright 1987
American Mathematical Society