Research

Research Interests

I study fluid PDEs, especially the free-boundary problems of inviscid fluids, such as water waves
with vorticity, magnetohydrodynamics(MHD), elastodynamics, relativistic fluids, etc.
• Nonlinear stability of compressible vortex sheets 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.
• Incompressible limit of free-surface inviscid fluids, including the case of initial data "not well-prepared". 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 inviscid fluids.

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

• [13] Jiawei Wang, Junyan Zhang. Incompressible Limit of Non-isentropic Elastodynamics with Ill-prepared Initial Data. In preparation.
• [12] Junyan Zhang. Nonlinear Stability and Incompressible Limit of 3D Current-Vortex Sheets with or without Surface Tension in Ideal MHD. In preparation.
• [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: 94 pp (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. Accepted by J. Math Pures Appl. arXiv: 2105.00596. [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): 124. (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 finished and released on April 12 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]
• [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]