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arXiv · 2307.10599

Remark on the ill-posedness for KdV-Burgers equation in Fourier amalgam spaces

Divyang G. Bhimani·Saikatul Haque
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Abstract

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 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 $p=q(\neq 2)$ and in modulation space $M_s^{2,q}$ which corresponds to the case $p=2,q\neq 2$.

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Divyang G. Bhimani, Saikatul Haque. 2023-07-20. Remark on the ill-posedness for KdV-Burgers equation in Fourier amalgam spaces. https://arxiv.org/abs/2307.10599

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