Scholarlink

<p>In this paper, we mainly study a new quasilinear shallow-water waves equation with or without the weakly dissipative effect on the circle, which can be formally derived from a model with the effect of underlying shear flow from the incompressible rotational two-dimensional shallow water in the moderately nonlinear regime by Wang, Kang and Liu (Appl. Math. Lett. 124:107607, 2022). The local well-posedness and precise blow-up criterion of the solutions to the equation are firstly obtained. Moreover, some sufficient conditions which guarantee the occurrence of blow-up of solutions are studied by constructing corresponding Riccati-type differential systems according to the different real-valued intervals in which the dispersive parameter <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(\theta \)</EquationSource> <EquationSource Format="MATHML"><math> <mi>θ</mi> </math></EquationSource> </InlineEquation> being located. Finally, we study the local-in-space blow-up criterion for the equation by utilizing the characteristic line method and energy estimates. It is worthy noting that we need to overcome the difficulty induced by the nonlocal nonlinear structure and different dispersive parameter ranges of equation to get corresponding piecewise convolution estimates on the circle.</p>

错误：搜索内容不能为空，请输入英文关键词
错误：关键词超出字数限制，请精简
高级检索

Blow-up criteria for a new periodic quasilinear shallow-water waves equation

  • 期刊论文

  • 发表日期：

    2026年3月10日

查看全文
  • Xiaofang Dong

摘要

In this paper, we mainly study a new quasilinear shallow-water waves equation with or without the weakly dissipative effect on the circle, which can be formally derived from a model with the effect of underlying shear flow from the incompressible rotational two-dimensional shallow water in the moderately nonlinear regime by Wang, Kang and Liu (Appl. Math. Lett. 124:107607, 2022). The local well-posedness and precise blow-up criterion of the solutions to the equation are firstly obtained. Moreover, some sufficient conditions which guarantee the occurrence of blow-up of solutions are studied by constructing corresponding Riccati-type differential systems according to the different real-valued intervals in which the dispersive parameter \(\theta \) θ being located. Finally, we study the local-in-space blow-up criterion for the equation by utilizing the characteristic line method and energy estimates. It is worthy noting that we need to overcome the difficulty induced by the nonlocal nonlinear structure and different dispersive parameter ranges of equation to get corresponding piecewise convolution estimates on the circle.