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February 11, 2026Proceedings of the American Mathematical Society0 citations

Optimal time decay of solution to the 𝑀₁ model

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NZNangao Zhang

Key Points

  • This research aims to analyze the global existence and asymptotic behavior of solutions to the M1 model's Cauchy problem.
  • Analyzed the Cauchy problem specific to the M1 model.
  • Established global existence under smallness conditions.
  • Utilized the time-weighted energy method for proving results.
  • Applied Lp-Lq estimates derived from Green's function analysis.
  • Demonstrated that the solution globally exists under certain conditions.
  • Showed that the solution approaches the equilibrium state at an optimal rate.
  • Found that this may be the first result regarding optimal decay in multi-dimensional settings.

Abstract

In this paper, we are concerned with the asymptotic behavior of solution to the Cauchy problem of M 1 M₁ 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 βˆ’ 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.

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Cite This Study

Nangao Zhang (2026) studied this question.

synapsesocial.com/papers/698c1cb3267fb587c655f504https://doi.org/10.1090/proc/17542
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