| 一维可压缩Navier-Stokes方程组整体弱解的存在性 |
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| 引用本文： | 孙美满. 一维可压缩Navier-Stokes方程组整体弱解的存在性[J]. 阜阳师范学院学报(自然科学版), 2013, 30(1): 1-3 |
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| 作者姓名： | 孙美满 |
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| 作者单位： | 武汉科技大学城市学院数学教研室,湖北武汉,430083 |
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| 基金项目： | 湖北省教育厅科学技术研究项目 |
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| 摘 要： | 研究了粘性依赖于密度的含外力项的一维可压缩Navier-Stokes方程组的自由边界问题。粘性系数μ(ρ)和压力P(ρ)为密度ρ的一般函数,并且外力项f为自变量x和t的函数。在适当的假设条件下,利用差分方法,得到了弱解的整体存在性和唯一性。为克服一般的粘性系数μ(ρ)和外力项f给研究带来的困难,文章得到了一些新的先验估计。
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| 关 键 词： | Navier-Stokes方程组 依赖于密度的粘性 外力 整体存在性 |
Existence of the weak solution of the one dimensional compressible Navier-Stokes equations |
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| SUN Mei-man. Existence of the weak solution of the one dimensional compressible Navier-Stokes equations[J]. Journal of Fuyang Teachers College:Natural Science, 2013, 30(1): 1-3 |
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| Authors: | SUN Mei-man |
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| Affiliation: | SUN Mei-man ( Teaching arrd Research Section of Mathematics, City College, Wt＆an University of Science and Technology, Wuhan Hubei 430083, China) |
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| Abstract: | The free boundary for one-dimensional compressible Navier-Stokes equations with density-dependent viscosity and extemal force is studied. Precisely, the viscosity coefficientμ（ρ） and the pressure P（ρ） are general functions of the densityρ , and the external forcefis function of independent variablexandt. Under certain assumptions, the global existence and uniqueness of the weak solution were obtained through the difference method. The present study obtains some new prior estimates for overcoming the difficulty in the similar research caused by the general viscosity coefficient μ（p） and the external forcef. |
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| Keywords: | Navier-Stokes equations density-dependent viscosity external force global existence. |
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