Propagation of oscillations to 2D incompressible Euler equations期刊界 All Journals 搜尽天下杂志传播学术成果专业期刊搜索期刊信息化学术搜索

Propagation of oscillations to 2D incompressible Euler equations

Authors:	Ping Zhang Guangrong Wu Qingjiu Qiu

Affiliation:	(1) Institute of Mathematics, Chinese Academy of Sciences, 100080 Beijing, China;(2) Department of Mathematics, Nanjing University, 210093 Nanjing, China

Abstract:	The asymptotic expansions are studied for the vorticity ${ omega ^ in (t,x)}$ to 2D incompressible Euler equations with-initial vorticity $omega _0^ in (x) = omega _0 (x) + varepsilon omega _0^1 left( {x,frac{{varphi _0 (x)}}{varepsilon }} right)$ , where ϕ₀(x) satisfies \|d ϕ₀(x)\|≠0 on the support of $omega _0^1 left( { cdot ,theta } right),theta in {rm T}$ and is sufficiently smooth and with compact support in ℝ² (resp. ℝ²×T) The limit,v(t,x), of the corresponding velocity fields {v ^ɛ(t,x)} is obtained, which is the unique solution of (E) with initial vorticity ω₀(x). Moreover, $omega ^ in (t,x) = omega (t,x) + varepsilon omega ^1 left( {t,x,frac{{varphi (t,x)}}{varepsilon }} right) + o(varepsilon ){text{ }}in{text{ }}C([0,infty ),{text{ L}}^p$ (ℤ²)) for all 1≽p∞, where $omega (t,x) = partial _1 upsilon _2 (t,x) - partial _2 upsilon _1 left( {t,x} right),omega ^1 (t,x,theta )$ and ϕ(t,x) satisfy some modulation equation and eikonal equation, respectively.

Keywords:	Incompressible Euler equations paradifferential calculus propagation of oscillations Young measures
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