Abstract：This paper is devoted to a highly nontrivial study of -order Fourier transform-based Riesz integral-differential calculus for Lorentz-Morrey spaces (covering Lebesgue spaces): (i) Riesz integral traces of Lorentz-Morrey spaces; (ii) Riesz differential equations in dual Lorentz-Morrey spaces; (iii) Riesz variational capacities for Lorentz-Morrey spaces.

成果2：

我院教师欧耀彬与东南大学杨璐老师合作的论文《Incompressible limit of all-time solutions to isentropic Navier-Stokes equations with ill-prepared data in bounded domains》在Journal of Differential Equations上发表。

论文链接：https://doi.org/10.1016/j.jde.2024.11.009

Abstract：In this paper, we study the incompressible limit of all-time strong solutions to the isentropic compressible Navier-Stokes equations with ill-prepared initial data and slip boundary condition in three-dimensional bounded domains. The uniform estimates with respect to both the Mach number and all time are derived by establishing a nonlinear integral inequality. In contrast to previous results for well-prepared initial data, the time derivatives of the velocity are unbounded which leads to the loss of strong convergence of the velocity. The novelties of this paper are to establish weighted energy estimates of new-type and to carefully combine the estimates for the fast variables and the slow variables, especially for the highest-order spatial derivatives of the fast variables. The convergence to the global strong solution of incompressible Navier-Stokes equations is shown by applying the Helmoltz decomposition and the strong convergence of the incompressible part of the velocity.

成果3：

我院教师潘迎利与哈尔滨工业大学李娜、苏颖教授合作的论文《Sharp Rate of the Accelerating Propagation for a Recursive System》在Studies in Applied Mathematics上发表。

论文链接：https://doi.org/10.1111/sapm.70029

Abstract：How to characterize the rate of accelerating propagation in recursive systems is a challenging topic though it has attracted great attention of theoretical and empirical ecologists. In this paper, we determine the sharp rate of accelerating propagation for a unimodal recursive system with a heavy-tailed dispersal kernel 𝐽 through tracking of level sets of solutions with compactly supported initial data. It turns out that the solution level set 𝐸𝜆(𝑛) satisfies 𝐽(𝐸𝜆(𝑛)) ∼ 𝑒−𝜌∗𝑛 for large 𝑛, where 𝜆 is the level and 𝜌∗ is determined by the linearized system at zero.