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

We have established (a weak form of) ill-posedness for the KdV-Burgers equation on a real line in Fourier amalgam spaces \(\widehat {w}_s^{p,q}\) 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 \(\mathcal {F}L_s^q\) which corresponds to the case \(p=q(\neq 2)\) and in modulation space \(M_s^{2,q}\) which corresponds to the case \(p=2,q\neq 2\) .