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 compressible flows, 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). This is also viewed as the singular limit of 1st-order symmetric hyperbolic systems whose (free) boundaries are characteristic.
  • 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.

  • [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]
  • [14] Jiawei Wang, Junyan Zhang. Low Mach Number Limit of Non-isentropic Inviscid Elastodynamics with General Initial Data. arXiv:2412.09941, preprint. [PDF]
  • Junyan Zhang. Existence, Nonlinear Stability and Incompressible Limit of Current-Vortex Sheets with or without Surface Tension in Compressible Ideal MHD. arXiv:2312.11254v2, 110 pages, [PDF]. This preprint is split into two parts for submission.
    • [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].
  • [11] Jiawei Wang, Junyan Zhang. Incompressible Limit of Compressible Ideal MHD Flows inside a Perfectly Conducting Wall. arXiv:2308.01142, preprint. [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].

  • Ph.D. thesis: Junyan Zhang. The Free-Boundary Problems in Inviscid Magnetohydrodynamics with or without Surface Tension. (292 pages, a summary of my MHD papers [1-3,5,7-9]) [DOI] [PDF].

  • [9] Xumin Gu, Chenyun Luo, Junyan Zhang. Zero Surface Tension Limit of the Free-Boundary Problem in Incompressible Magnetohydrodynamics. Nonlinearity, 35(12), 6349-6398 (2022). arXiv: 2109.05400. [DOI] [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].
  • [5] Junyan Zhang. Local well-posedness of the Free-Boundary Problem in Compressible Resistive Magnetohydrodynamics. Calc. Var. Partial Differ. Equ., 62(4), no.124: 1-60 (2023). arXiv: 2012.13931. [DOI] [PDF].
  • [4] Chenyun Luo, Junyan Zhang. Local Well-posedness for the Motion of a Compressible Gravity Water Wave with Vorticity. J. Differ. Eq., Vol.332, 333-403 (2022). arXiv: 2109.02822. (This paper was first released and submitted on 12 April 2020) [DOI] [PDF]
  • [3] Junyan Zhang. A priori Estimates for the free-boundary problem of Compressible Resistive MHD Equations and Incompressible Limit. arXiv: 1911.04928, preprint. [PDF] (not sent for publication)
  • [2] Chenyun Luo, Junyan Zhang. A priori Estimates for the Incompressible Free-Boundary Magnetohydrodynamics Equations with Surface Tension. SIAM J. Math. Anal., 53(2), 2595-2630 (2021). arXiv: 1907.11827. [DOI] [PDF]
  • [1] Chenyun Luo, Junyan Zhang. A Regularity Result for the Incompressible Magnetohydrodynamics Equations with Free Surface Boundary. Nonlinearity, 33(4), 1499–1527 (2020). arXiv: 1904.05444 . [DOI] [PDF]


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