text: The Cauchy problem for the 1d Kuramoto–Sivashinsky equation is well-posed in the sense of Hadamard—that is, for given initial data , there exists a unique solution  that depends continuously on the initial data.
  The 1d Kuramoto–Sivashinsky equation possesses Galilean invariance—that is, if  is a solution, then so is , where  is an arbitrary constant. Physically, since  is a velocity, this change of variable describes a transformation into a frame that is moving with constant relative velocity . On a periodic domain, the equation also has a reflection symmetry: if  is a solution, then  is also a solution.