Global solutions to the lake equations with isolated vortex regions

Author:
Chaocheng Huang

Journal:
Quart. Appl. Math. **61** (2003), 613-638

MSC:
Primary 76B03; Secondary 35Q35, 86A05

DOI:
https://doi.org/10.1090/qam/2019615

MathSciNet review:
MR2019615

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Abstract: The vorticity formulation for the lake equations in is studied. We assume that the initial vorticity has the form , where the initial vortex region is a domain and . It is shown that the Cauchy problem can be formulated as an integral system. Global existence and uniqueness of the solution to the integral system are established. Consequently, the lake equation admits a unique weak solution, global in time, in the form of , where and .

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DOI:
https://doi.org/10.1090/qam/2019615

Article copyright:
© Copyright 2003
American Mathematical Society