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Solution of equations describing thin layer flow of heavy viscous liquid on a curvilinear surface. (English. Russian original) Zbl 0907.76021
Mosc. Univ. Mech. Bull. 51, No. 6, 8-11 (1996); translation from Vestn. Mosk. Univ., Ser. I 1996, No. 6, 32-36 (1996).
The authors consider the system of differential equations
\[\frac{\partial u}{\partial t} + u \frac{\partial u}{\partial x} + v \frac{\partial u}{\partial y} = A(x) + \frac{\partial^2 u}{\partial y^2},\quad \frac{\partial u}{\partial x} + \frac{\partial v}{\partial y} = 0\],
\[\frac{\partial u}{\partial y} = 0, \quad v = \frac{\partial h}{\partial t} + u \frac{\partial h}{\partial x}\text{ for }y=h(t,x), \quad v=0\text{ for }y = 0\]
which describes an non-stationary flow of a thin layer of heavy viscous liquid on a fixed impenetrable surface. The problem is reduced to the Cauchy problem for equations with a smaller number of variables.
MSC:
76D99 Incompressible viscous fluids
35Q35 PDEs in connection with fluid mechanics
Keywords:
Cauchy problem
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