  The present work provides well-posedness and exponential decay results for
the Blackstock-Crighton-Kuznetsov equation arising in the modeling of nonlinear
acoustic wave propagation in thermally relaxing viscous fluids. First, we treat
the associated linear equation by means of operator semigroups. Moreover, we
derive energy estimates which we will use in a fixed-point argument in order to
obtain well-posedness of the Blackstock-Crighton-Kuznetsov equation. Using a
classical barrier argument we prove exponential decay of solutions.
