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三维可压流Stokes近似系统的唯一可解性 被引量：4

Unique solvability of the stokes approximation equations for three-dimensional compressible flows
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摘要 研究三维有界光滑区域上的Stokes近似系统的唯一可解性问题。首先考虑线性化系统强解的全局存在性,其次通过线性化系统构造迭代逼近系统,并对迭代逼近系统的强解做一致估计;最后得到迭代逼近解序列的收敛性。证明了当初始值满足一个兼容性条件时Stokes近似系统初边值问题局部强解的存在唯一性。 The unique solvability of the Stokes approximation equations onto a three-dimensional bounded smooth domain is studied.The global existence of the strong solution to linearized equations is firstly considered.Then the iterative approximation system has been constructed by linearized system and its strong solution has been uniformly estimated.The convergence of the sequence of iterative approximation is concluded.The unique existence of the local strong solution to the initial boundary value problem for the Stokes approximation equations is investigated when the initial date satisfies a natural compatibility condition.
作者 郭蒙 郭真华
机构地区 西北大学数学系
出处 《黑龙江大学自然科学学报》 CAS 北大核心 2010年第5期611-618,共8页 Journal of Natural Science of Heilongjiang University
基金 国家自然科学基金资助项目(10771170)
关键词 三维可压流Stokes近似系统 局部强解 唯一可解性 3D compressible stokes approximation equations local strong solution unique solvability
分类号 O175.2 [理学—基础数学]
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参考文献17

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同被引文献23

  • 1Zhen-hua Guo.Large-time Behavior of Solutions to the Stokes Approximation Equations for Two Dimensional Compressible Flows[J].Acta Mathematicae Applicatae Sinica,2005,21(4):637-654. 被引量：2
  • 2袁洪君,佟丽宁.一类带有真空的不可压Navier-Stokes方程的局部古典解[J].吉林大学学报（理学版）,2007,45(3):381-382. 被引量：4
  • 3Vaigant V A, Kazhikhov A V. Global Solutions to the Potential Flow equations for a compressible Viscous Fluids at Small Reynolds Numbers[J]. Diff Eq, 1994 (30): 935-946.
  • 4Min L, Kazhikhov A V, Ukai S. Global solutions to the Cauchy problem of the Stokes Approximation equations for the two-dimensional compressible fluids [J]. Comm PDE, 1998, 23:985-1006.
  • 5Guo Z, Jiang S, Li J. Global helically symmetric solutions to the Stokes Approximations equations for thress-dimensional compressible viscous flow [J]. Methods and applications of analysis, 2005 ( 2 ): 135-152.
  • 6Li J, Xin Z. Some uniform estimates and blow up behavior global strong solutions to the Stokes approximation equation for two-dimensional compressible flows[J]. Diff Eq, 2006 ( 221 ): 275-308.
  • 7Eeireisl E, Novotny A, Petzeltova H. On the Existence of Globally defined weak solutions to the Navier-Stokes equations[J]. Math Fluid Mech, 2001 (3) : 358-392.
  • 8JIANG S, ZHANG P. Axisymmetric solutions of the 3D Navier-Stokes for compressible isentropic fluid [ J ]. Math Pure Appl,2003, 82 : 949-973.
  • 9SUN W, JIANG S, GUO Z. Helically solutions symmetric solutions to the 3D Navier-Stokes for compressible isen- tropic fluid[J]. Diff Eq, 2006, 222: 263-296.
  • 10JIANG S, ZHANG P. Global spherically symmetric solu- tions of the compressible isentropic Navier-Stokes equa- tions[J]. Comm Math Phy, 2001, 215: 559-581.

引证文献4

二级引证文献1

黑龙江大学自然科学学报
2010年 第5期

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