Strong Solutions of the Navier–Stokes Equations for Nonhomogeneous Incompressible Fluids
Strong Solutions of the Navier–Stokes Equations for Nonhomogeneous Incompressible Fluids
复制标题
DOI：
10.1081/pde-120021191
复制
发表时间：
2003-01
影响因子：
1.9
通讯作者：
Hi Jun Choe;Hyunseok Kim
中科院分区：
文献类型：
--
作者：
Hi Jun Choe;Hyunseok Kim
摘要本文研究了非均匀不可压缩流体Navier-Stokes方程在Ω <$R3中的强解。通过导出与密度下界无关的先验估计，证明了初值问题（Ω = R3）或初边值问题（Ω ≠ R3）的局部强解的存在唯一性，即使初始密度在Ω的开子集中为零，也是如此，存在初始真空。作为先验估计的直接结果，我们得到了局部强解的一个延拓定理。
Abstract We study strong solutions of the Navier–Stokes equations for nonhomogeneous incompressible fluids in Ω ⊂ R 3. Deriving higher a priori estimates independent of the lower bounds of the density, we prove the existence and uniqueness of local strong solutions to the initial value problem (for Ω =R 3) or the initial boundary value problem (for Ω ⊂ ⊂ R 3) even though the initial density vanishes in an open subset of Ω, i.e., an initial vacuum exists. As an immediate consequence of the a priori estimates, we obtain a continuation theorem for the local strong solutions.