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Global well-posedness and polynomial stability for the chemotaxis-fluid systems in Marcinkiewicz spaces

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2025年5月14日

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Pham Truong Xuan,
Nguyen Thi Van,
Le The Sac

摘要

In this paper, we study the global existence, uniqueness and polynomial stability of mild solutions for the Keller–Segel–Navier–Stokes system in the framework of Marcinkiewicz spaces, i.e., weak- $L^p$ $L^{p}$ spaces $L^{p,\infty }(\mathbb {R}^d)$ $L^{p, \infty} (R^{d})$ , where $d \geqslant 4$ $d ⩾ 4$ . In our strategy, we first combine the $L^{p,d_1}-L^{q,d_2}$ $L^{p, d_{1}} - L^{q, d_{2}}$ heat estimates and Yamazaki-type estimates of the heat semigroup with fixed point arguments to obtain the global well-posedness of mild solutions by using a fixed point lemma. Then, we establish a polynomial stability of such solutions.