Remark on the Ill-Posedness for KdV-Burgers Equation in Fourier Amalgam Spaces

Abstract

We have established (a weak form of) ill-posedness for the KdV-Burgers equation on a real line in Fourier amalgam spaces w^sp,q with s<−1. The particular case p=q=2 recovers the result in Molinet and Ribaud (Int. Math. Res. Not. 2002:1979–2005 (2002)). The result is new even in Fourier Lebesgue space ℱLsq which corresponds to the case p=q(≠2) and in modulation space Ms2,q which corresponds to the case p=2,q≠2.