  We prove a global well-posedness and regularity result of strong solutions to
a slightly modified Michelson-Sivashinsky equation in any spatial dimension and
in the absence of physical boundaries. Local-in-time well-posedness (and
regularity) in the space $W^{1,\infty}(\mathbb{R}^d)$ is established and is
shown to be global if in addition the initial data is either periodic or
vanishes at infinity. The proof of the latter result utilizes ideas previously
introduced by Kiselev, Nazarov, Volberg and Shterenberg to handle the
critically dissipative surface quasi-geostrophic equation and the critically
dissipative fractional Burgers equation. Namely, the global regularity result
is achieved by constructing a time-dependent modulus of continuity that must be
obeyed by the solution of the initial-value problem for all time, preventing
blowup of the gradient of the solution. This work provides an example where
regularity is shown to persist even when a-priori bounds are not available.
