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arXiv · 2404.05127

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

Hao Chen·Gastón Vergara-Hermosilla·Jihong Zhao
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Abstract

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 $L^{p}$-$L^{q}$ 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.

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Hao Chen, Gastón Vergara-Hermosilla, Jihong Zhao. 2024-04-08. Well-posedness of the 2D surface quasi-geostrophic equation in variable Lebesgue spaces. https://arxiv.org/abs/2404.05127

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