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http://dx.doi.org/10.14403/jcms.2010.23.2.271

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)
Publication Information
Journal of the Chungcheong Mathematical Society / v.23, no.2, 2010 , pp. 271-277 More about this Journal
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 ${\mathbb{R}}^2$.
Keywords
global existence; perfect incompressible fluid; Besov space; vorticity;
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