His dissertation was titled Convergence of Particle Methods for Euler and Boltzmann Equations with Oscillatory Solutions.
[1] Hou is known for his research on multiscale analysis and singularity formation of the three-dimensional incompressible Euler and Navier-Stokes equations.
In 2014, Hou and his former postdoc, Guo Luo, presented convincing numerical evidence that the axisymmetric Euler equations develop finite time singularity from smooth initial data.
[4] In 2022, Hou and his former Ph.D. student, Jiajie Chen, made a breakthrough[citation needed] by proving the finite time singularity of the axisymmetric Euler equations with smooth data and boundary (the so-called Hou-Luo blowup scenario).
[5][6] Hou’s recent work on the potentially singular behavior of the three-dimensional Navier-Stokes equations has also generated a lot of interests.
His early work on the convergence of the point vortex method for incompressible Euler equations was unexpected and considered a breakthrough[citation needed].