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<p>In this paper, we establish the existence and uniqueness of mild solutions defined on the whole line time-axis of Boussinesq systems on the weak-Lorentz spaces with Muckenhoupt weight. First, we use the weighted dispersive (and smoothing) estimates and interpolation functors to prove Yamazaki-type inequality and establish the existence of the bounded mild solutions defined on the whole line time-axis for the corresponding linear systems. Then, we use the results of linear systems and fixed-point arguments to establish the existence and uniqueness of mild solutions for Boussinesq systems. In addition, we prove a Massera-type principle to establish the existence of almost periodic mild solutions. Finally, we prove the polynomial stability of such mild solutions.</p>

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Well-posedness of the Boussinesq systems on whole line time-axis and on weighted spaces

  • 期刊论文

  • 发表日期：

    2025年2月17日

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  • Pham Truong Xuan,
  • Tran Thi Ngoc

摘要

In this paper, we establish the existence and uniqueness of mild solutions defined on the whole line time-axis of Boussinesq systems on the weak-Lorentz spaces with Muckenhoupt weight. First, we use the weighted dispersive (and smoothing) estimates and interpolation functors to prove Yamazaki-type inequality and establish the existence of the bounded mild solutions defined on the whole line time-axis for the corresponding linear systems. Then, we use the results of linear systems and fixed-point arguments to establish the existence and uniqueness of mild solutions for Boussinesq systems. In addition, we prove a Massera-type principle to establish the existence of almost periodic mild solutions. Finally, we prove the polynomial stability of such mild solutions.