AI 中文总结
该研究是两部分工作的第一部分，针对二维半空间中具对数敏感性的趋化性-Navier-Stokes系统，通过渐近展开得到边界层剖面并建立其适定性，还解决扩散项消失问题建立超临界趋化性-Euler方程解的局部适定性。
AI 中文摘要
这是关于二维半空间中趋化性-Navier-Stokes系统边界层收敛性的两部分工作的第一部分。本文研究了Navier滑移边界条件下具有对数奇异性的趋化性-Navier-Stokes系统，更准确地说，我们对粘性系数ε>0的趋化性-Navier-Stokes系统进行了精确渐近展开，得到了部分边界层剖面，建立了相应边界层剖面的适定性。特别地，我们还克服了扩散项消失带来的困难，建立了超临界趋化性-Euler方程（ε=0时）解的局部适定性。
英文摘要
This is the first part of a two-part work concerning the boundary layer convergence for chemotaxis-Navier-Stokes system in a two-dimensional half-space. In this paper, we investigate the chemotacxis-Navier-Stokes system with the logarithmic singularity under Navier-slip boundary conditions. More precisely, we perform an exact asymptotic expansion for the chemotaxis Navier-Stokes system with viscous coefficient $\varepsilon>0$, and obtain partial boundary layer profiles, establishing the well-posedness of the corresponding boundary layer profiles. Specially, we also establish the local well-posedness of solutions to the supercritical chemotaxis Euler equation (with $\varepsilon=0$) by overcoming the difficulty from the disappearance of diffusion terms.
