Well-posedness of the 2D surface quasi-geostrophic equation in variable Lebesgue spaces

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发表日期：

2025年6月2日

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Hao Chen,
Gaston Vergara-Hermosilla,
Jihong Zhao

摘要

In this paper, we are mainly concerned with the well-posedness of the dissipative surface quasi-geostrophic equation in the framework of variable Lebesgue spaces. Based on some analytical results developed in the variable Lebesgue spaces and the $L^{p}$ $L^{p}$ - $L^{q}$ $L^{q}$ decay estimates of the fractional heat kernel, we establish the local existence and regularity of solutions to the 2D dissipative surface quasi-geostrophic equation in the variable Lebesgue space.