Research
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Research Interests

I study fluid PDEs, especially the freeboundary problems of inviscid fluids, such as water waves
 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 1storder symmetric hyperbolic systems.
 Incompressible limit of freesurface inviscid fluids, including the case of initial data "not wellprepared". This is also viewed as the singular limit of 1storder symmetric hyperbolic systems whose (free) boundaries are characteristic.
 Singularity or longtime evolution of freesurface inviscid fluids.
with vorticity, magnetohydrodynamics(MHD), elastodynamics, relativistic fluids, etc.
You may find all of my papers (preprint versions) on arXiv or researchgate.
 [13] Jiawei Wang, Junyan Zhang. Incompressible Limit of Nonisentropic Elastodynamics with Illprepared Initial Data. In preparation.
 [12] Junyan Zhang. Nonlinear Stability and Incompressible Limit of 3D CurrentVortex 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 GravityCapillary Water Waves with Vorticity: Local Wellposedness, Incompressible and ZeroSurfaceTension Limits. arXiv: 2211.03600, preprint. [PDF].
Ph.D. thesis: Junyan Zhang. The FreeBoundary Problems in Inviscid Magnetohydrodynamics with or without Surface Tension. (292 pages. A summary of my MHD papers [13,5,79].) [DOI] [PDF] .
 [9] Xumin Gu, Chenyun Luo, Junyan Zhang. Zero Surface Tension Limit of the FreeBoundary Problem in Incompressible Magnetohydrodynamics. Nonlinearity, 35(12), 63496398 (2022). arXiv: 2109.05400. [DOI] [PDF].
 [8] Hans Lindblad, Junyan Zhang. Anisotropic Regularity of the FreeBoundary 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 wellposedness of the FreeBoundary Incompressible Magnetohydrodynamics with Surface Tension. Accepted by J. Math Pures Appl. arXiv: 2105.00596. [PDF].
 [6] Junyan Zhang. Local wellposedness and Incompressible Limit of the FreeBoundary Problem in Compressible Elastodynamics. Arch. Rational Mech. Anal., 244(3), 599697 (2022). arXiv: 2102.07979. [DOI] [PDF].
 [5] Junyan Zhang. Local wellposedness of the FreeBoundary 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 Wellposedness for the Motion of a Compressible Gravity Water Wave with Vorticity. J. Differ. Eq., Vol.332, 333403 (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 freeboundary 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 FreeBoundary Magnetohydrodynamics Equations with Surface Tension. SIAM J. Math. Anal., 53(2), 25952630 (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]