# 英国代考|MATH0015 Fluid Mechanics 流体力学

where
$$S^{\prime}(Z)=-\frac{3}{2} \frac{\frac{5}{3} P(Z)-Z P^{\prime}(Z)}{Z^{2}} \text { for all } Z>0$$
The reader will have noticed that the bulk viscosity has been neglected in $(7.10)$ for the sake of simplicity.

As always in this book, equations (7.5-7.8) are interpreted in the weak sense specified in Chapter 1 (see Section $7.2$ below). We recall that the technical restrictions imposed on the constitutive functions are dictated by the existence theory developed in Chapter 3 and could be relaxed, to a certain extent, as far as the singular limit passage is concerned.

As indicated in the introductory part, the geometry of the physical domain plays a crucial role in the study of propagation of the acoustic waves. As already pointed out, the existence of an effective mechanism of dissipation of the acoustic waves is intimately linked to solvability of the (overdetermined) system (7.4) that can be written in a more concise form as
$$-\Delta_{x} r=\Lambda r \text { in } \Omega, \frac{\lambda^{2}}{\omega}=-\Lambda,\left.\nabla_{x} r\right|_{o n}=0$$

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