Research

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Research Interests

    I study PDEs arising from fluid dynamics. Currently I am focusing on the following areas:
  • Nonlinear stability of compressible vortex sheets and contact discontinuities in various kinds of fluids with or without surface tension. This is also viewed as the stability of characteristic strong discontinuities for 1st-order symmetric hyperbolic systems.
  • Singular limits of various types of fluid PDEs, including the low Mach number limit for "ill-prepared data"(especially the free-boundary problems), multi-parameter singular limits (e.g., low Mach number and small Alfven number limits for MHD).
  • Singularity or long-time evolution of free-surface fluids.
Publications and Preprints

You may find all of my papers (preprint versions) on arXiv or researchgate or Google Scholar.

Total: 15    Published: 9    Submitted: 5    Not sent for publication: 1

Below are selected publications. Click here for the full list of publications.

  • [15] Qiangchang Ju, Jiawei Wang, Junyan Zhang. Uniform Anisotropic Regularity and Low Mach Number Limit of Non-isentropic Ideal MHD Equations with a Perfectly Conducting Boundary. arXiv:2412.09943, preprint. [PDF]
  • [13] Junyan Zhang. On the Incompressible Limit of Current-Vortex Sheets with or without Surface Tension. arXiv:2405.00421. [PDF].
  • [12] Junyan Zhang. Well-posedness and Incompressible Limit of Current-Vortex Sheets with Surface Tension in Compressible Ideal MHD. arXiv:2312.11254v3. [PDF].
  • [10] Chenyun Luo, Junyan Zhang. Compressible Gravity-Capillary Water Waves with Vorticity: Local Well-posedness, Incompressible and Zero-Surface-Tension Limits. arXiv: 2211.03600, preprint. [PDF].
  • [8] Hans Lindblad, Junyan Zhang. Anisotropic Regularity of the Free-Boundary Problem in Compressible Ideal Magnetohydrodynamics. Arch. Rational Mech. Anal., 247(5), no.89: 1-94 (2023). arXiv: 2106.12173. [DOI] [PDF].
  • [7] Xumin Gu, Chenyun Luo, Junyan Zhang. Local well-posedness of the Free-Boundary Incompressible Magnetohydrodynamics with Surface Tension. J. Math Pures Appl., Vol. 182, 31-115 (2024). arXiv: 2105.00596. [DOI] [PDF].
  • [6] Junyan Zhang. Local well-posedness and Incompressible Limit of the Free-Boundary Problem in Compressible Elastodynamics. Arch. Rational Mech. Anal., 244(3), 599-697 (2022). arXiv: 2102.07979. [DOI] [PDF].
  • [4] Chenyun Luo, Junyan Zhang. Local Well-posedness for the Motion of a Compressible Gravity Water Wave with Vorticity. J. Differ. Equ., Vol.332, 333-403 (2022). arXiv: 2109.02822. (This paper was first released and submitted on 12 April 2020) [DOI] [PDF]