59 citations · 152 across the 16 of their papers we have counts for
16 papers
Self-similar finite-time blowups with singular profiles of the generalized Constantin-Lax-Majda model: theoretical and numerical investigations
De Huang, Jiajun Tong, Xiuyuan Wang
We investigate novel scenarios of self-similar finite-time blowups of the generalized Constantin-Lax-Majda model with a parameter , which are induced by a new setting where the…
The Immersed Boundary Problem in 2-D: the Navier-Stokes Case
Jiajun Tong, Dongyi Wei
We study the immersed boundary problem in 2-D. It models a 1-D elastic closed string immersed and moving in a fluid that fills the entire plane, where the fluid motion is governed…
Geometric Properties of the 2-D Peskin Problem
Jiajun Tong, Dongyi Wei
The 2-D Peskin problem describes a 1-D closed elastic string immersed and moving in a 2-D Stokes flow that is induced by its own elastic force. The geometric shape of the string an…
On self-similar finite-time blowups of the De Gregorio model on the real line
De Huang, Jiajun Tong, Dongyi Wei
We show that the De Gregorio model on the real line admits infinitely many compactly supported, self-similar solutions that are distinct under rescaling and will blow up in finite…
Global Solutions to the Tangential Peskin Problem in 2-D
Jiajun Tong
We introduce the tangential Peskin problem in 2-D, which is a scalar drift-diffusion equation with a nonlocal drift. It is derived with a new Eulerian perspective from a special se…
Tumor Growth with Nutrients: Regularity and Stability
Matt Jacobs, Inwon Kim, Jiajun Tong
In this paper we study a tumor growth model with nutrients. The model presents dynamic patch solutions due to the contact inhibition among the tumor cells. We show that when the nu…
Darcy's Law with a Source term
Matt Jacobs, Inwon Kim, Jiajun Tong
We introduce a novel variant of the JKO scheme to approximate Darcy's law with a pressure dependent source term. By introducing a new variable that implicitly controls the source t…
The -contraction principle in optimal transport
Matt Jacobs, Inwon Kim, Jiajun Tong
In this work, we use the JKO scheme to approximate a general class of diffusion problems generated by Darcy's law. Although the scheme is now classical, if the energy density is sp…
Interface Dynamics in a Two-phase Tumor Growth Model
Inwon Kim, Jiajun Tong
We study a tumor growth model in two space dimensions, where proliferation of the tumor cells leads to expansion of the tumor domain and migration of surrounding normal tissues int…
Regularized Stokes Immersed Boundary Problems in Two Dimensions: Well-posedness, Singular Limit, and Error Estimates
Jiajun Tong
Inspired by the numerical immersed boundary method, we introduce regularized Stokes immersed boundary problems in two dimensions to describe regularized motion of a 1-D closed elas…
Directed migration of microscale swimmers by an array of shaped obstacles: modeling and shape optimization
Jiajun Tong, Michael J. Shelley
Achieving macroscopic directed migration of microscale swimmers in a fluid is an important step towards utilizing their autonomous motion. It has been experimentally shown that dir…
On the Viscous Camassa-Holm Equations with Fractional Diffusion
Zaihui Gan, Fang-Hua Lin, Jiajun Tong
We study Cauchy problem of a class of viscous Camassa-Holm equations (or Lagrangian averaged Navier-Stokes equations) with fractional diffusion in both smooth bounded domains and i…
Solvability of the Stokes Immersed Boundary Problem in Two Dimensions
Fang-Hua Lin, Jiajun Tong
We study coupled motion of a 1-D closed elastic string immersed in a 2-D Stokes flow, known as the Stokes immersed boundary problem in two dimensions. Using the fundamental solutio…
Guiding microscale swimmers using teardrop-shaped posts
Megan S. Davies Wykes, Xiao Zhong, Jiajun Tong +6
The swimming direction of biological or artificial microscale swimmers tends to be randomised over long time-scales by thermal fluctuations. Bacteria use various strategies to bias…
Stability of Soft Quasicrystals in a Coupled-Mode Swift-Hohenberg Model for Three-Component Systems
Kai Jiang, Jiajun Tong, Pingwen Zhang
In this article, we discuss the stability of soft quasicrystalline phases in a coupled-mode Swift-Hohenberg model for three-component systems, where the characteristic length scale…
Stability of Two-Dimensional Soft Quasicrystals
Kai Jiang, Jiajun Tong, Pingwen Zhang +1
The relative stability of two-dimensional soft quasicrystals is examined using a recently developed projection method which provides a unified numerical framework to compute the fr…