Global smooth solutions of the equations of a viscous, heat-conducting, one-dimensional gas with density-dependent viscosity. (English) Zbl 0927.35014
The author investigates initial-boundary value problems for the equations of a one-dimensional motion of a viscous, heat-conducting gas. The viscosity \(\mu\) depends on density and goes to zero as density goes to zero. If this decrease does not happen too rapidly, e.g. if \(\mu(u)= u^{-\lambda}\) and \(\lambda\in (0,1/4)\), then the author shows existence of global smooth solutions. This extends previous work of the reviewer, in which \(\mu(u)\geq \mu_0>0\) was assumed instead. [B. Kawohl, J. Differ. Equations 58, 76-103 (1985; Zbl 0579.35052)].
Reviewer: B.Kawohl (Köln)
MSC:
| 35B45 | A priori estimates in context of PDEs |
| 35A05 | General existence and uniqueness theorems (PDE) (MSC2000) |
| 35L50 | Initial-boundary value problems for first-order hyperbolic systems |
| 76N15 | Gas dynamics (general theory) |
| 76N10 | Existence, uniqueness, and regularity theory for compressible fluids and gas dynamics |
| 35Q30 | Navier-Stokes equations |
Citations:
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