Research

I am interested in anything that is related to PDEs. However, I have mostly been working with those PDEs that involve harmonic analysis in one way or another.

My research focuses on topics related to the wave turbulence theory and random initial data problem. Meanwhile, I am also interested in various topics in fluid dynamics, including fluid stability and singularity, especially the inviscid damping problem and construction of singularities problem.

Publication list:

• Y. Deng, Z. Hani, and X. Ma, “Hilbert’s sixth problem: Derivation of fluid equations via boltzmann’s kinetic theory”, arXiv preprint arXiv:2503.01800, 2025.

• Y. Deng, Z. Hani, and X. Ma, “Long time derivation of the boltzmann equation from hard sphere dynamics”, arXiv preprint arXiv:2408.07818, 2024.

• X. Ma, “Almost sharp wave kinetic theory of multidimensional KdV type equations with d ≥ 3”, arXiv preprint arXiv:2204.06148, 2022.

• X. Ma, “Linear stability of the 2D irrotational circulation flow around an elliptical cylinder”, SIAM Journal on Mathematical Analysis, vol. 54, no. 5, pp. 5576–5587, 2022.

• K. Jin and X. Ma, “Cancellations of resonances and long time dynamics of cubic Schrödinger equation on T”, Communications in Mathematical Physics, vol. 381, no. 3, pp. 1309–1368, 2021.