近年来致力于可压缩Navier-Stokes方程、不可压缩Navier-Stokes和相关方程的研究。已发表学术论文300多篇，其中SCI收录240余篇。主要成就包括：
1、用偏微分方程的弱收敛方法、补偿紧理论和弱解成立的能量等式研究了一维可压缩磁流体方程弱解的剪切粘性系数的零极限问题，改进了著名数学家H. Frid和V. V. Shelukhin不考虑磁场效应时的工作；
2、将不可压Navier-Stokes方程中某些知名的正则性准则作了本质改进；
3、研究了不可压Navier-Stokes方程的稳定性理论，解决了周勇教授的一个问题；
4、首次提出双调和波映照的概念，得到了波映照和双调和波映照的正则性准则；
5、改进了日本著名数学家T. Ogawa的关于调和映照热流问题的正则性准则；
6、证明了超导方程弱解的存在唯一性。
[1] Fan JS, Jiang S, Nakamura G., On logarithmically improved regularity criteria for the Navier-Stokes equations in R-n, IMA JOURNAL OF APPLIED MATHEMATICS, 出版年: APR 2011 卷: 76 期: 2 页: 298-311。
[2] Fan JS, Sawada O，Regularity criteria for the Euler equations with nondecaying data，NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS，出版年: FEB 15 2011，卷: 74 期: 4 页: 1393-1401。
[3] Fan JS, Gao HJ，Uniqueness of weak solutions in critical space of the 3-D time-dependent Ginzburg-Landau equations for superconductivity，MATHEMATISCHE NACHRICHTEN，出版年: AUG 2010，卷: 283 期: 8 页: 1134-1143。
[4] Fan JS, Jiang S, Nakamura G, INVERSE PROBLEM OF A TIME-DEPENDENT GINGZBURG-LANDAU MODEL FOR SUPERCONDUCTIVITY WITH THE FINAL OVERDETERMINATION, OSAKA JOURNAL OF MATHEMATICS, 出版年: MAR 2010, 卷: 47 期: 1 页: 89-108。
[5] Fan JS, Ozawa T, Global Cauchy Problem for the 2-D Magnetohydrodynamic-alpha Models with Partial Viscous Terms, JOURNAL OF MATHEMATICAL FLUID MECHANICS, 出版年: MAY 2010, 卷: 12 期: 2 页: 306-319。
[6] Fan JS, Ozawa T, UNIQUENESS OF WEAK SOLUTIONS TO THE CAUCHY PROBLEM FOR THE 3-D TIME-DEPENDENT GINZBURG-LANDAU MODEL FOR SUPERCONDUCTIVITY, DIFFERENTIAL AND INTEGRAL EQUATIONS, 出版年: JAN-FEB 2009, 卷: 22 期: 1-2 页: 27-34。
[7] Fan JS, Di Cristo M, Jiang Y, et al. Inverse viscosity problem for the Navier-Stokes equation, JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 出版年: MAR 15 2010, 卷: 365 期: 2 页: 750-757。
[8] Fan JS, Jiang S, Ou YB, A blow-up criterion for compressible viscous heat-conductive flows, ANNALES DE L INSTITUT HENRI POINCARE-ANALYSE NON LINEAIRE, 出版年: JAN-FEB 2010, 卷: 27 期: 1 页: 337-350。
[9] Fan JS, Jiang S, Ni GX, UNIFORM BOUNDEDNESS OF THE RADIALLY SYMMETRIC SOLUTIONS OF THE NAVIER-STOKES EQUATIONS FOR ISENTROPIC COMPRESSIBLE FLUIDS, OSAKA JOURNAL OF MATHEMATICS, 出版年: SEP 2009, 卷: 46 期: 3 页: 863-876。
[10] Fan JS, Ozawa T, Logarithmically improved regularity criteria for Navier-Stokes and related equations, MATHEMATICAL METHODS IN THE APPLIED SCIENCES, 出版年: NOV 30 2009, 卷: 32 期: 17 页: 2309-2318。
[11] Fan JS, Ozawa T, REGULARITY CRITERIA FOR A SIMPLIFIED ERICKSEN-LESLIE SYSTEM MODELING THE FLOW OF LIQUID CRYSTALS, DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS, 出版年: NOV 2009, 卷: 25 期: 3 页: 859-867。
[12] Fan JS, Ozawa T, REGULARITY CRITERIA FOR THE MAGNETOHYDRODYNAMIC EQUATIONS WITH PARTIAL VISCOUS TERMS AND THE LERAY-alpha-MHD MODEL, KINETIC AND RELATED MODELS, 出版年: JUN 2009, 卷: 2 期: 2 页: 293-305。
[13] Fan J, Nakamura G, Well-posedness of an inverse problem of Navier-Stokes equations with the final overdetermination, JOURNAL OF INVERSE AND ILL-POSED PROBLEMS, 出版年: AUG 2009, 卷: 17 期: 6 页: 565-584。
[14] Fan JS, Gao HJ, REGULARITY CONDITIONS FOR THE 3D NAVIER-STOKES EQUATIONS, QUARTERLY OF APPLIED MATHEMATICS, 出版年: 2009, 卷: 67 期: 1 页: 195-199。
[15] Fan JS, Jiang Y, Nakamura G, Inverse problems for the Boussinesq system, INVERSE PROBLEMS, 出版年: AUG 2009, 卷: 25 期: 8 文献编号: 085007。
[16] Fan JS, Ozawa T, Regularity criterion for a Bona-Colin-Lannes system, NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 出版年: OCT 1 2009, 卷: 71 期: 7-8 页: 2634-2639。
[17] Fan JS, Gao HJ, UNIQUENESS OF WEAK SOLUTIONS TO A MODEL OF ELECTRO-KINETIC FLUID, COMMUNICATIONS IN MATHEMATICAL SCIENCES, 出版年: JUN 2009, 卷: 7 期: 2 页: 411-421。
[18] Fan JS, Zhou Y, A note on regularity criterion for the 3D Boussinesq system with partial viscosity, APPLIED MATHEMATICS LETTERS, 出版年: MAY 2009, 卷: 22 期: 5 页: 802-805。
[19] Fan JS, Gao HJ, Uniqueness of weak solutions to a non-linear hyperbolic system in electrohydrodynamics, NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 出版年: MAR 15 2009, 卷: 70 期: 6 页: 2382-2386。
[20] Fan JS, Ozawa T, Regularity criteria for the 3D density-dependent Boussinesq equations, NONLINEARITY, 出版年: MAR 2009, 卷: 22 期: 3 页: 553-568。
[21] Fan JS, Nakamura G, Local solvability of an inverse problem to the density-dependent Navier-Stokes equations, APPLICABLE ANALYSIS, 出版年: 2008, 卷: 87 期: 10-11 页: 1255-1265。
[22] Fan JS, Yu WH, Global variational solutions to the compressible magnetohydrodynamic equations, NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 出版年: NOV 15 2008, 卷: 69 期: 10 页: 3637-3660。
[23] Fan JS, Guo BL, Regularity criterion to some liquid crystal models and the Landau-Lifshitz equations in R-3, SCIENCE IN CHINA SERIES A-MATHEMATICS, 出版年: OCT 2008, 卷: 51 期: 10 页: 1787-1797。
[24] Fan JS, Jiang S, Ni GX, On regularity criteria for the n-dimensional Navier-Stokes equations in terms of the pressure, JOURNAL OF DIFFERENTIAL EQUATIONS, 出版年: JUN 1 2008, 卷: 244 期: 11 页: 2963-2979。
[25] Fan JS, Ozawa T, Asymptotic stability for the Navier-Stokes equations, JOURNAL OF EVOLUTION EQUATIONS, 出版年: MAY 2008, 卷: 8 期: 2 页: 379-389。
[26] Fan JS, Jiang S, Blow-up criteria for the Navier-Stokes equations of compressible fluids, JOURNAL OF HYPERBOLIC DIFFERENTIAL EQUATIONS, 出版年: MAR 2008, 卷: 5 期: 1 页: 167-185。
[27] Fan J, Yu WH, Strong solution to the compressible magnetohydrodynamic equations with vacuum, NONLINEAR ANALYSIS-REAL WORLD APPLICATIONS, 出版年: FEB 2009, 卷: 10 期: 1 页: 392-409。
[28] Fan JS, Gao HJ, Stability of weak solutions to the compressible Navier-Stokes equations in bounded annular domains, MATHEMATICAL METHODS IN THE APPLIED SCIENCES, 出版年: JAN 25 2008, 卷: 31 期: 2 页: 179-192。
[29] Fan JS, Jiang S, Nakamura G, Vanishing shear viscosity limit in the magnetohydrodynamic equations, COMMUNICATIONS IN MATHEMATICAL PHYSICS, 出版年: MAR 2007, 卷: 270 期: 3 页: 691-708。
