我们讨论了Oseen方程当对流函数的散度不为零时弱解和强解的存在性.利用Lax-Milgram定理, 证明了在空间H1(Ω)中弱解的存在性.在此基础上, 应用重复迭代及对偶原理等方法进一步证明了在一般的Sobolev空间中弱解和强解的存在性,并得到相应的解的不等式估计.
Abstract
We deal with the existence of weak and strong solutions for Oseen equations in the case that the divergence of convective vector is nonzero. Using Lax-Milgram Theorem, we first prove the existence of weak solution in H1(Ω), and then on the basis of this result, we use methods of iterative and dual principle to prove the existence of weak and strong solutions in generic Sobolev spaces and obtain corresponding estimates for these solutions.
关键词
很弱解 /
弱解 /
强解 /
Oseen方程
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Key words
very weak solution /
weak solution /
strong solution /
Oseen equation
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参考文献
[1] Amrouche C., Rodrguez-Bellido M. A., Stationary Stokes, Oseen and Navier-Stokes equations with singular data, Arch. Retional Mech. Anal., 2011, 199: 597-651.
[2] Temam R., Infinite-Dimensional System in Mechanics and Physics, Springer-Verlag, New York, 1988.
[3] Amrouche C., Girault V., Decomposition of vector space and application to the Stokes problem in arbitrary dimension, Czechoslovak Mathematical Journal, 1994, 44: 109-140.
[4] Cattabriga L., Su un problema al contorno relativo al sistema di equazoni di Stokes, Rend. Sem. Univ. Padova., 1961, 31: 308-340.
[5] De Rham G., Variétés Différentiables, Hermann, Paris, 1960.
[6] Adams R. A., Sobolev Spaces, Pure and Applied Mathematics 65, Academic Press, New York, London, 1975.
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脚注
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基金
国家自然科学基金资助项目(11041004);黑龙江省自然科学基金项目(A200913)
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