TY - JOUR

T1 - Viscous fluid flow in a layer with a free boundary

AU - Zhuravleva, E. N.

N1 - Funding Information: This work was supported by the Russian Foundation for Basic Research (Grant No. 19-01-00096). Publisher Copyright: © 2022, Pleiades Publishing, Ltd.

PY - 2022/6

Y1 - 2022/6

N2 - A partially invariant solution of a three-dimensional problem with a free boundary for the Navier–Stokes equations is studied. The flow domain under consideration is a horizontal layer bounded by a solid plane from below and by a flat free surface from above. The vertical velocity and pressure are independent of the x and y coordinates. Three flow modes can be formed for different initial velocities of the flow: stabilization to the quiescent state with time, solution blow up within a finite time, and self-similar regime in which the layer thickness unboundedly increases with time.

AB - A partially invariant solution of a three-dimensional problem with a free boundary for the Navier–Stokes equations is studied. The flow domain under consideration is a horizontal layer bounded by a solid plane from below and by a flat free surface from above. The vertical velocity and pressure are independent of the x and y coordinates. Three flow modes can be formed for different initial velocities of the flow: stabilization to the quiescent state with time, solution blow up within a finite time, and self-similar regime in which the layer thickness unboundedly increases with time.

KW - Navier–Stokes equations

KW - problems with a free boundary

KW - self-similar solution

KW - solution blow up

UR - http://www.scopus.com/inward/record.url?scp=85137549390&partnerID=8YFLogxK

UR - https://www.mendeley.com/catalogue/f809f190-b857-3c12-91c2-967c8e7156ed/

U2 - 10.1134/S0021894422030026

DO - 10.1134/S0021894422030026

M3 - Article

AN - SCOPUS:85137549390

VL - 63

SP - 383

EP - 391

JO - Journal of Applied Mechanics and Technical Physics

JF - Journal of Applied Mechanics and Technical Physics

SN - 0021-8944

IS - 3

ER -