AI 中文总结
研究在纳维滑移边界条件下球形刚体在不可压缩粘性流体中的线性化运动，利用球体几何正则性，为相应流固算子建立正则性等估计，为构建非线性系统的强\(W^{2,1}_q\)解和加藤型解提供基础。
AI 中文摘要
我们研究了在具有摩擦的纳维滑移边界条件下，浸没在占据整个空间的不可压缩粘性流体中的球形刚体的线性化运动。对于无滑移情况，半群正则性和衰减估计已被充分理解，但在滑移情况下此类结果仅限于有界域。通过利用球体的几何正则性，我们为相应的流固算子建立了强\(L^q\)正则性、有界解析性和精确的\(L^q - L^r\)估计。这些结果将为构建相应非线性系统的强\(W^{2,1}_q\)解和加藤型解提供基础。
英文摘要
We study the linearized motion of a spherical rigid body immersed in an incompressible viscous fluid occupying the whole space, under Navier slip boundary conditions with friction. While semigroup regularity and decay estimates are well understood for the no-slip case, such results have been limited to bounded domains in the slip setting. By exploiting the geometric regularity of the sphere, we establish strong $L^q$-regularity, bounded analyticity, and sharp $ L^q-L^r$ estimates for the corresponding fluid-structure operator. These results would provide a foundation for constructing strong $W^{2,1}_q$ solutions and Kato-type solutions to the corresponding nonlinear system.
