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Classical Solutions for a Generalized Euler Equation in Two Dimensions

✍ Scribed by Marcel Oliver

Publisher
Elsevier Science
Year
1997
Tongue
English
Weight
226 KB
Volume
215
Category
Article
ISSN
0022-247X

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✦ Synopsis

It is well known that the Euler equations in two spatial dimensions have global classical solutions. We provide a new proof which is analytic rather than geometric. It is set in an abstract framework that applies to the so-called lake and the great lake equations describing weakly non-hydrostatic effects of bottom topography on the motion of shallow water. The key ingredient is a new L p estimate on the nonlinear term. The estimate is used to develop a global H m theory for bounded domains in ‫ޒ‬ 2 which is similar in spirit to a 1975 paper by R. Temam. It also m Ž . provides explicit bounds on the H norm which grow like exp exp t .

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