Local well-posedness for a Cauchy problem associated to a non linear evolution equation - Milla Garcia, Luis (2021)
In this article we will study the local well-posedness for a non-linear Cauchy problem associated with the differential equation KdV- Kuramoto-Sivashinsky: in the infinite dimensional spaces (periodic sobolev) H sper. We do this using the theory of C0- semigrupos, main properties of the Fourier transform in H sper, as the inmersions in these spaces and that H s-1per is a Banach algebra, which allows us to justify the presence of the non-linearity .