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/

Zendy Plus

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

Zendy Tools

Zendy Open

In Hele-Shaw flows at vanishing surface tension, the boundary of a viscousfluid develops cusp-like singularities. In recent papers [1, 2] we have showedthat singularities trigger viscous shocks propagating through the viscousfluid. Here we show that the weak solution of the Hele-Shaw problem describingviscous shocks is equivalent to a semiclassical approximation of a special realsolution of the Painleve I equation. We argue that the Painleve I equationprovides an integrable deformation of the Hele-Shaw problem which describesflow passing through singularities. In this interpretation shocks appear asStokes level-lines of the Painleve linear problem.

Viscous shocks in Hele-Shaw flow and Stokes phenomena of the Painleve I transcendent