Concentrated steady vorticities of the Euler equation on 2-d domains and their linear stability

We consider concentrated vorticities for the Euler equation on a smooth domain $\mathrm{\Omega }?{\mathbf{R}}^2$ in the form of

$\omega =\sum _{j=1}^N{\omega }_j{\chi }_{{\mathrm{\Omega }}_j},|{\mathrm{\Omega }}_j|=\pi r_j^2,\underset{{\mathrm{\Omega }}_j}{\int }{\omega }_{j}d\mu ={\mu }_j\ne 0,$

supported on well-separated vortical domains ${\mathrm{\Omega }}_j$, $j=1,\dots ,N$, of small diameters $O(r_j)$. A conformal mapping framework is set up to study this free boundary problem with ${\mathrm{\Omega }}_j$ being part of unknowns. For any given vorticities ${\mu }_1,\dots ,{\mu }_N$ and small $r_1,\dots ,r_N\in {\mathbf{R}}^{+}$, through a perturbation approach, we obtain such piecewise constant steady vortex patches as well as piecewise smooth Lipschitz steady vorticities, both concentrated near non-degenerate critical configurations of the Kirchhoff–Routh Hamiltonian function. When vortex patch evolution is considered as the boundary dynamics of $?{\mathrm{\Omega }}_j$, through an invariant subspace decomposition, it is also proved that the spectral/linear stability of such steady vortex patches is largely determined by that of the 2N-dimensional linearized point vortex dynamics, while the motion is highly oscillatory in the 2N-codim directions corresponding to the vortical domain shapes.     

Condensation of all-cis-tetraphenylcyclotetrasiloxanetetraol in ammonia: new method for preparation of ladder-like polyphenylsilsesquioxanes

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Triacetic acid lactone as a bioprivileged molecule in organic synthesis

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Synthesis and antimycobacterial activity of purine conjugates with (S)-lysine and (S)-ornithine

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Stability of O3 + N2, O3 + O2 and O3 + CO2 double hydrates: DFT study

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PXI在测控系统中的应用

随着有关PXI总线的规范和产品的推出，由于优良的性能指标和适宜的价格，使其受到各相关行业的广泛关注。对风洞测控系统的结构和系统配置作了具体的阐述，并对PXI总线在具体使用中的效果和特点作了较详细的介绍。     

以人为本的教学理念与高校体育教学

以人为本的教学理念是现代教育影响最大的教育思想之一，它更注重情感教育和创新教育．从教学情境、课程内容、教学方法和学生学习方式人手，本文对以人为本的教学理念与高校体育教学进行了研究．