  Unsteady evolution of an inviscid bubble, surrounded by a viscous fluid
moving with velocity $V$ far from the bubble, in a Hele-Shaw channel is
described by a general class of exact solutions obtained without surface
tension. Several numerical examples are provided. These solutions select the
bubble velocity $U = 2V$ in a long-time asymptotics from a continuum of all
possible values of $U$, because the selected value is shown to represent the
only attractor of this infinitely-dimensional nonlinear dynamical system. This
work is an expanded version of results announced earlier by two of us
(Phys.~Rev.~E {\bf 89}, 061003(R), 2014).
