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Overview

Daomin Cao is a researcher affiliated with the Chinese Academy of Sciences in China. Their work spans primarily in the field of Mathematics with additional contributions to Engineering. Cao's research focuses mainly on Applied Mathematics and Mathematical Physics, with significant exploration in Computational Mechanics, Computational Theory and Mathematics, and Statistical and Nonlinear Physics.

The research topics covered by Cao include:

  • Navier-Stokes equation solutions
  • Advanced Mathematical Physics Problems
  • Nonlinear Partial Differential Equations
  • Advanced Mathematical Modeling in Engineering
  • Geometric Analysis and Curvature Flows
  • Nonlinear Waves and Solitons
  • Fluid Dynamics and Turbulent Flows

Cao has published extensively, with a notable number of papers appearing in venues such as:

  • arXiv (Cornell University)
  • Journal of Differential Equations
  • Calculus of Variations and Partial Differential Equations
  • Transactions of the American Mathematical Society
  • Journal of Functional Analysis

Recent publications highlight the diversity and depth of Cao's work, including:

  • Desingularization of Vortices for Two-Dimensional Steady Euler Flows via the Vorticity Method (2020, SIAM Journal on Mathematical Analysis)
  • Standing waves with prescribed mass for the Schrödinger equations with van der Waals type potentials (2020, Journal of Differential Equations)
  • Traveling vortex pairs for 2D incompressible Euler equations (2021, Calculus of Variations and Partial Differential Equations)
  • The number of positive solutions to the Brezis-Nirenberg problem (2021, Transactions of the American Mathematical Society)
  • Nonlinear Stability of Planar Vortex Patches in an Ideal Fluid (2021, Journal of Mathematical Fluid Mechanics)

Cao frequently collaborates with several coauthors, including Guolin Qin, Weicheng Zhan, Changjun Zou, Jie Wan, and Tujin Kim. The collaborative efforts have resulted in a consistent output of research contributions, particularly in topics related to fluid dynamics, nonlinear equations, and mathematical modeling.

Best Publications

  • Nontrivial Solution of Semilinear Elliptic Equations with Critical Exponent in R

    D. M. Cao

  • Solutions for semilinear elliptic equations with critical exponents and Hardy potential

    Daomin Cao;Pigong Han

  • A note on the sign-changing solutions to elliptic problems with critical Sobolev and Hardy terms $

    Daomin Cao;Shuangjie Peng

  • The asymptotic behaviour of the ground state solutions for Hénon equation

    Daomin Cao;Shuangjie Peng

  • Infinitely many solutions for p-Laplacian equation involving critical Sobolev growth

    Daomin Cao;Shuangjie Peng;Shusen Yan

  • Solutions to critical elliptic equations with multi-singular inverse square potentials

    Daomin Cao;Pigong Han

  • Solutions with multiple peaks for nonlinear elliptic equations

    Daomin Cao;Ezzat S. Noussair;Shusen Yan

  • Infinitely many solutions for an elliptic problem involving critical Sobolev growth and Hardy potential

    Daomin Cao;Shusen Yan

  • Non-autonomous dynamics of wave equations with nonlinear damping and critical nonlinearity

    Chunyou Sun;Chunyou Sun;Daomin Cao;Jinqiao Duan

  • THE CONCENTRATION-COMPACTNESS PRINCIPLE IN NONLINEAR ELLIPTIC EQUATIONS

    Xiping Zhu;Daomin Cao

  • Multiplicity of positive and nodal solutions for nonlinear elliptic problems in $\mathbb {R}^N$

    Daomin Cao;Ezzat S. Noussair

  • Planar vortex patch problem in incompressible steady flow

    Daomin Cao;Shuangjie Peng;Shusen Yan

  • Regularization of Point Vortices Pairs for the Euler Equation in Dimension Two

    Daomin Cao;Zhongyuan Liu;Juncheng Wei

  • Semi-Classical Bound States for Schrödinger Equations with Potentials Vanishing or Unbounded at Infinity

    Daomin Cao;Shuangjie Peng

  • Uniqueness of positive bound states with multi-bump for nonlinear Schrödinger equations

    Daomin Cao;Shuanglong Li;Peng Luo

  • ON THE EXISTENCE AND NODAL CHARACTER OF SOLUTIONS OF SEMILINEAR ELLIPTIC EQUATIONS

    Daomin Cao;Xiping Zhu

  • Existence and uniqueness results on Single-Peaked solutions of a semilinear problem

    Daomin Cao;Ezzat S. Noussair;Shusen Yan

  • Global attractivity of positive periodic solution to periodic Lotka–Volterra competition systems with pure delay

    Xianhua Tang;Daomin Cao;Xingfu Zou

  • Existence and uniqueness of multi-bump bound states of nonlinear Schrödinger equations with electromagnetic fields

    Daomin Cao;Zhongwei Tang

  • On the existence and profile of multi-peaked solutions to singularly perturbed semilinear Dirichlet problems

    Daomin Cao;Norman E. Dancer;Ezzat S. Noussair;Shunsen Yan

Frequent Co-Authors

Jinqiao Duan
Jinqiao Duan Great Bay University
Juncheng Wei
Juncheng Wei Chinese University of Hong Kong
Gui-Qiang Chen
Gui-Qiang Chen University of Oxford
Xingfu Zou
Xingfu Zou University of Western Ontario

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