Optimal time decay of solution to the 𝑀₁ model

Nangao Zhang

doi:10.1090/proc/17542

Optimal time decay of solution to the 𝑀₁ model

Proceedings of the American Mathematical Society 2026

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Authors: Nangao Zhang

DOI: 10.1090/proc/17542

Cited by: 0

References: 14

Abstract

In this paper, we are concerned with the asymptotic behavior of solution to the Cauchy problem of M 1 M_{1} model. Under some smallness conditions, we show that the solution to this system exists globally and tends time-asymptotically to the corresponding equilibrium state at the optimal rate. The proof is based on both the time-weighted energy method and the L p − L q L^{p}-L^{q} estimates from the detailed analysis of the Green’s function. To the best of our knowledge, this may be the first result regarding the optimal decay of solution to this model in the multi-dimensional case.

Fields of Study & Subjects

Advanced Mathematical Physics Problems Navier-Stokes equation solutions Stability and Controllability of Differential Equations

Publication details

Journal / source: Proceedings of the American Mathematical Society
Volume: 154
Issue: 4
Pages: 1721–1734
Publication date: 9 February 2026
Language: EN

References 14