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 ${\hat{w}}_s^{p,q}$ with $s<-1$. The particular case $p=q=2$ recovers the result of L. Molinet and F. Ribaud [Int. Math. Res. Not., (2002), pp. 1979-2005]. The result is new even in Fourier Lebesgue space $\mathcal{F}{L}_s^q$ which corresponds to the case $p=q(\ne 2)$ and in modulation space $M_s^{2,q}$ which corresponds to the case $p=2,q\ne 2$.