Propagation of oscillations to 2D incompressible Euler equations

Autor: Qingjiu Qiu, Guangrong Wu, Ping Zhang
Rok vydání: 1998
Předmět:
Zdroj: Science in China Series A: Mathematics. 41:449-460
ISSN: 1862-2763
1006-9283
DOI: 10.1007/bf02879933
Popis: 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\(\omega _0 \left( x \right)(resp. \omega _0^1 (x,\theta ))\) 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.
Databáze: OpenAIRE
Externí odkaz: