| 柳洪志,袁洪君,李梵蓓,乔节增.一类带有非牛顿位势的可压缩Navier-Stokes方程整体强解的存在性[J].数学年刊A辑,2011,32(4):407~422 |
| 一类带有非牛顿位势的可压缩Navier-Stokes方程整体强解的存在性 |
| Global Existence of Strong Solutions to Compressible Navier-Stokes Equations with Non-Newtonian Potential |
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| DOI： |
| 中文关键词: Navier-Stokes方程 可压缩 强解 非牛顿位势 |
| 英文关键词:Navier-Stokes equation Compressible Strong solution Non-Newtonian potential |
| 基金项目:国家自然科学基金(No10971080)资助的项目 |
| Author Name | Affiliation | E-mail | | LIU Hongzhi | Institute of Mathematics, Jilin University, Changchun 130012, China
School of Statistics and Mathematics, Inner Mongolia Finance and Economics College, Huhhot 010051, China. | school-32@163.com | | YUAN Hongjun | College of Mathematics, Jilin University, Changchun 130012, China. | hjy@jlu.edu.cn | | LI Fanbei | School of Statistics and Mathematics, Inner Mongolia Finance and Economics College, Huhhot 010051, China. | liuhz08@mails.jlu.edu.cn | | QIAO Jiezeng | School of Statistics and Mathematics, Inner Mongolia Finance and Economics College, Huhhot 010051, China. | nmgqjz@163.com |
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| 中文摘要: |
| 主要研究了一类带有非牛顿位势的可压缩Navier-Stokes方程:
$$
\rho_t+(\rho u)_x=0, & \mbox{在} \ (0,T) \times (0,1) \ \mbox{内,}
(\rho u)_t+(\rho u^2)_x+\rho \Phi_x-(\mu(\rho)u_x)_x+P_x=0, & \mbox{在} \ (0,T) \times (0,1) \ \mbox{内,}
\ds ((\Phi_x^2+\mu_0)^{\frac{p-2}{2}}\Phi_x)_x=4\pi g\Big(\rho-\frac{1}{|\Omega|}\int_\Omega \rho \d x\Big), & \mbox{在} \ (0,T) \times (0,1) \ \mbox{内,}
$$
其中粘性系数$\mu$依赖于密度$\rho$, $\Phi$是非牛顿位势.证明了上述问题的强解的存在性. 在相容性条件下, 得到了强解的唯一性. |
| 英文摘要: |
| The authors study a class of the isentropic compressible Navier-Stokes equations in one dimension:
$$
\rho_t+(\rho u)_x=0, & \mbox{in} \ (0,T) \times (0,1),
(\rho u)_t+(\rho u^2)_x+\rho \Phi_x-(\mu(\rho)u_x)_x+P_x=0, & \mbox{in} \ (0,T) \times (0,1),
\ds ((\Phi_x^2+\mu_0)^{\frac{p-2}{2}}\Phi_x)_x=4\pi g\Big(\rho-\frac{1}{|\Omega|}\int_\Omega \rho \d x\Big), & \mbox{in} \ (0,T) \times (0,1),
$$
where the viscosity coefficient $\mu$ depends on density $\rho$, and $\Phi$ is a non-Newtonian potential.
The authors prove the existence of strong solutions for the problem and obtain the uniqueness under the compatiblity condition. |
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