English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

In order to describe behavior of various liquid-like materials at highpressures, incompressible fluid models with pressure dependent viscosity seemto be a suitable choice. In the context of implicit constitutive relationsinvolving the Cauchy stress and the velocity gradient these models areconsistent with standard procedures of continuum mechanics. Understandingmathematical properties of governing equations is connected with various typesof idealization, some of them lead to studies in unbounded domains. In thispaper, we first bring up several characteristic features concerning fluids withpressure dependent viscosity. Then we study three-dimensional flows of a classof fluids with the viscosity depending on the pressure and the shear rate. Bymeans of higher differentiability methods we establish large data existence ofa weak solution for the Cauchy problem. This seems to be a first result thatanalyzes flows of considered fluids in unbounded domains. Even in the contextof purely shear rate dependent fluids of a power-law type the result presentedhere improves some of earlier works.

Unsteady Flows of Fluids with Pressure Dependent Viscosity in Unbounded Domains