  Hydrodynamic discontinuities in an external potential and incompressible flow
are investigated. Using the reaction front as an example in a 2D stream, an
overdetermined system of equations is obtained that describes its motion in
terms of the surface itself. Assuming that the harmonic flux approaching
discontinuity is additional smooth, these equations can be used to determine
the motion of this discontinuity without taking into account the influence of
the flow behind the front, as well as the entire external flow. It is well
known that for vanishingly low viscosity, the integral relation on the boundary
(Dirichlet, Neumann problems) connects the tangential and normal components of
the velocity. Knowing one of them along the boundary of the discontinuity, one
can determine the entire external flow. However, assuming the external flow is
smooth, this will also be the case for all derivatives of velocity with respect
to coordinates and time. Then a paradox arises, knowing the position of the
discontinuity and the velocity data at a point on its surface, it is possible
to determine the motion of this discontinuity without taking into account the
influence of the flow behind the front, as well as the entire external flow.
There is no physical explanation for this mechanism. It is possible that a
boundary layer is formed in front of the front, where viscosity plays a
significant role and Euler equations are violated. It is argued that the
classical idea of the motion of hydrodynamic discontinuities in the smooth,
potential and incompressible flow in the external region should be supplemented
in this case.
