Global existence of the radially symmetric solutions of the Navier–Stokes equations for the isentropic compressible fluids
Global existence of the radially symmetric solutions of the Navier–Stokes equations for the isentropic compressible fluids
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DOI：
10.1002/mma.545
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发表时间：
2005-01
影响因子：
2.9
通讯作者：
H. Choe;Hyunseok Kim
中科院分区：
文献类型：
--
作者：
H. Choe;Hyunseok Kim
本文研究了环形区域中具有径向对称数据的等熵可压缩Navier-Stokes方程。我们首先证明了具有非负有界密度的径向对称弱解的整体存在性和正则性结果。然后证明了当初值ρ0，u 0满足相容条件$$-\mu \Delta {\rm \bf u}_{0} -（\lambda + \mu）\nabla \，{\rm div}\，{\rm \bf u}_{0} + \nabla（A\rho_{0}^{\gamma}）=\rho_{0}^{1/2}{\rm \bf g}$$对于某个径向对称g ∈ L2。初始密度ρ0不必为正。我们还证明了强解的一些唯一性结果。版权所有© 2004年约翰威利父子有限公司。
We study the isentropic compressible Navier–Stokes equations with radially symmetric data in an annular domain. We first prove the global existence and regularity results on the radially symmetric weak solutions with non‐negative bounded densities. Then we prove the global existence of radially symmetric strong solutions when the initial data ρ0, u0 satisfy the compatibility condition $$-\mu \Delta {\rm \bf u}_{0} -(\lambda + \mu)\nabla \,{\rm div}\,{\rm \bf u}_{0} + \nabla (A\rho_{0}^{\gamma})=\rho_{0}^{1/2}{\rm \bf g}$$ for some radially symmetric g ∈ L2. The initial density ρ0 needs not be positive. We also prove some uniqueness results on the strong solutions. Copyright © 2004 John Wiley & Sons, Ltd.