Theory of multipolar fluids. (English) Zbl 0815.76009

Nečas, Jindřich

Jentsch, Lothar (ed.) et al., Problems and methods in mathematical physics. 10th Conference, 10th TMP, TU of Chemnitz-Zwickau in Chemnitz, Germany, September 13-17, 1993. Leipzig: Teubner. Teubner-Texte Math. 134, 111-119 (1994).

The author works in the framework of the theory of multipolar viscous fluids by J. Necas and M. Silhavy [Q. Appl. Math. 49, No. 2, 247-265 (1991; Zbl 0732.76003)]. The paper shows that the theory provides a proof of the existence of global (in time) solutions even in circumstances when such a proof is not possible for Stokes linear stress- strain relation. Weak solutions for tripolar compressible isothermal gases are considered, where a singular limit to dipolar gas is possible. The specification for dipolar isothermal gas or for dipolar incompressible non-Newtonian fluids is considered as well as the singular limit to monopolar fluids.
For the entire collection see [Zbl 0796.00021].

Reviewer: D.Jou (Bellaterra)

MSC:

76A05

Non-Newtonian fluids

Keywords:

existence of global in time solutions; weak solutions; tripolar compressible isothermal gases; singular limit; dipolar isothermal gas

Citations:

Zbl 0732.76003