论文标题
在粘性可压缩液中的小刚体运动
On the motion of a small rigid body in a viscous compressible fluid
论文作者
论文摘要
我们考虑浸入3维欧几里生空间中的粘性压缩液中的小刚性物体的运动。假设对象是一个小半径$ \ varepsilon $的球，我们表明流体的行为不受渐近极限$ \ varepsilon \ to 0 $的对象的影响。结果适用于等等压力定律$ p（\ varrho）= a \ varrho^γ$对于任何$γ> \ frac {3} {2} $，在与刚体密度的轻度假设下。特别是，后者可能会在$γ> 3 $的情况下进行界定。 证明使用了一种新的方法来构建测试功能，以薄弱的问题的表述，尤其是所谓的Bogovskii操作员的新形式。
We consider the motion of a small rigid object immersed in a viscous compressible fluid in the 3-dimensional Eucleidean space. Assuming the object is a ball of a small radius $\varepsilon$ we show that the behavior of the fluid is not influenced by the object in the asymptotic limit $\varepsilon \to 0$. The result holds for the isentropic pressure law $p(\varrho) = a \varrho^γ$ for any $γ> \frac{3}{2}$ under mild assumptions concerning the rigid body density. In particular, the latter may be bounded as soon as $γ> 3$. The proof uses a new method of construction of the test functions in the weak formulation of the problem, and, in particular, a new form of the so-called Bogovskii operator.
