Journal of the Chungcheong Mathematical Society (충청수학회지)

The Chungcheong Mathematical Society (충청수학회)
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GLOBAL VORTICITY EXISTENCE OF A PERFECT INCOMPRESSIBLE FLUID IN B0∞,1(ℝ2)∩Lp(ℝ2)

  • Pak, Hee Chul (Department of Applied Mathematics and Institute of Basic Sciences Dankook University) ;
  • Kwon, Eun-Jung (Department of Applied Mathematics Dankook University)
  • Received : 2010.02.28
  • Accepted : 2010.04.23
  • Published : 2010.06.30
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Abstract

We prove the global (in time) vorticity existence for the 2-D Euler equations of a perfect incompressible fluid in $B^0_{{\infty},1}({\mathbb{R}}^2){\cap}L^p({\mathbb{R}}^2)$ with 1 < p < 2. Moreover, we prove that the particle trajectory map X(x, t) satisfies the following estimate: for some positive constant C $${\parallel}X^{\pm1}(\cdot,\;t)-id(\cdot){\parallel}_{B^1_{\infty,1}}{\leq}Ce^{e^{Ct}}$$, where id represents the identity map on ${\mathbb{R}}^2$.

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Acknowledgement

Supported by : Dankook University

References

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