Blow up of smooth highly decreasing at infinity solutions to the compressible Navier-Stokes equations
Blow up of smooth highly decreasing at infinity solutions to the compressible Navier-Stokes equations
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DOI：
10.1016/j.jde.2008.07.007
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发表时间：
2008-04
影响因子：
2.4
通讯作者：
O. Rozanova
中科院分区：
文献类型：
--
作者：
O. Rozanova
我们证明，在 3 维或更大维空间的情况下，即使初始数据不紧支持，具有守恒总质量、有限总能量和有限惯性动量的 Navier-Stokes 方程的柯西问题的平滑解也会在有限时间内失去初始平滑性。还考虑了等熵和不可压缩流体的情况。
We prove that the smooth solutions to the Cauchy problem for the Navier–Stokes equations with conserved total mass, finite total energy and finite momentum of inertia lose the initial smoothness within a finite time in the case of space of dimension 3 or greater even if the initial data are not compactly supported. The cases of isentropic and incompressible fluids are also considered.