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Demonstrates norm inflation in solutions of the critical equation, suggesting limitations in data-to-solution maps.
We consider the critical dissipative surface quasi-geostrophic equation on R² or T². Despite global regularity of the equation, we show that the data-to-solution map at the critical level H¹ is not uniformly bounded. We construct solutions that experience H¹ norm inflation from smooth, compactly supported initial data with large H¹ norm. We also demonstrate small-data norm inflation in supercritical Sobolev spaces Wβ ,p for $1<p<2$ and 1≤ β <2/p.
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Guo et al. (2026) studied this question.
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