Strong solutions to a modified Michelson-Sivashinsky equation

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