主要成果

1. 张立群等在OLEINIK猜想研究方面取得进展;
2. 关于一般的能量一致有界的阿尔法调和映照序列其收敛产生泡泡时是否成立能量不等式是一个源自Sacks-Uhlenbeck文章的公开问题, 王友德等对此问题构造了一个使得能量不等式成立的反例; 同时，他们对另一个公开问题“从标准二维球面进入一个紧黎曼流形的调和映射的能量是否存在间隙现象?”也构造一个反例;
3. 吉敏等对随机偏微分方程取得重要进展;
4. 李天虹等在eikonal方程方面取得进展;
5. 郝成春对物理真空可压缩Euler方程的自由边界问题取得进展;
6. 黄祥娣等证明了变粘性系数的3维非均匀不可压缩Navier-Stokes方程整体小解的适定性;证明可压缩等熵球对称流体和完全可压缩球对称流体光滑解的爆破都集中在球心附近;
7. 当流体粘性系数(在常数附近)依赖于密度函数时,3维非均匀不可压缩Navier-Stokes方程整体小解适定性;
8. 邓雯等证明了一类变系数二阶微分算子关于两个横截的特征曲面的唯一连续延拓性质;
9. 张平等证明了2, 3维不可压缩磁流体力学方程组整体小解的存在性;并证明当流体粘性系数(在常数附近)依赖于密度函数时,2维非均匀不可压缩Navier-Stokes方程整体适定性; 同时对经典不可压缩Navier-Stokes方程构造了一类大解.

中心成员2015年发表文章15篇,具体如下:

[1] Li, Yuxiang; Wang, Youde A counterexample to the energy identity for sequences of α  -harmonic maps. Pacific J. Math. 274 (2015), no. 1, 107–123.

[2] Huang, Wen; Ji, Min; Liu, Zhenxin; Yi, Yingfei Steady states of Fokker-Planck equations: II. Non-existence. J. Dynam. Differential Equations 27 (2015), no. 3-4, 743–762.

[3] Huang, Wen; Ji, Min; Liu, Zhenxin; Yi, Yingfei Steady states of Fokker-Planck equations: I. Existence. J. Dynam. Differential Equations 27 (2015), no. 3-4, 721–742.

[4] Huang, Wen; Ji, Min; Liu, Zhenxin; Yi, Yingfei Integral identity and measure estimates for stationary Fokker-Planck equations. Ann. Probab. 43 (2015), no. 4, 1712–1730.

[5] Hao, Chengchun Remarks on the free boundary problem of compressible Euler equations in physical vacuum with general initial densities. Discrete Contin. Dyn. Syst. Ser. B 20 (2015), no. 9, 2885–2931.

[6] Huang, Xiangdi; Wang, Yun Global strong solution of 3D inhomogeneous Navier-Stokes equations with density-dependent viscosity. J. Differential Equations 259 (2015), no. 4, 1606–1627.

[7] Huang, Xiangdi On formation of singularity of spherically symmetric nonbarotropic flows. Kyoto J. Math. 55 (2015), no. 1, 1–15.

[8] Huang, Xiangdi; Matsumura, Akitaka A characterization on breakdown of smooth spherically symmetric solutions of the isentropic system of compressible Navier-Stokes equations. Osaka J. Math. 52 (2015), no. 1, 271–283. 

[9] Abidi, Hammadi; Zhang, Ping Global smooth axisymmetric solutions of 3-D inhomogeneous incompressible Navier-Stokes system. Calc. Var. Partial Differential Equations 54 (2015), no. 3, 3251–3276.

[10] Paicu, Marius; Zhang, Ping On some large global solutions to 3-D density-dependent Navier-Stokes system with slow variable: well-prepared data. Ann. Inst. H. Poincaré Anal. Non Linéaire 32 (2015), no. 4, 813–832.

[11] Lin, Fanghua; Xu, Li; Zhang, Ping Global small solutions of 2-D incompressible MHD system. J. Differential Equations 259 (2015), no. 10, 5440–5485.

[12]Abidi, Hammadi; Zhang, Ping On the global well-posedness of 2-D inhomogeneous incompressible Navier-Stokes system with variable viscous coefficient. J. Differential Equations 259 (2015), no. 8, 3755–3802.

[13] Abidi, Hammadi; Zhang, Ping Global well-posedness of 3-D density-dependent Navier-Stokes system with variable viscosity. Sci. China Math. 58 (2015), no. 6, 1129–1150.

[14] Chemin, Jean-Yves; Zhang, Ping Remarks on the global solutions of 3-D Navier-Stokes system with one slow variable. Comm. Partial Differential Equations 40 (2015), no. 5, 878–896.

[15] Xu, Li; Zhang, Ping Global small solutions to three-dimensional incompressible magnetohydrodynamical system. SIAM J. Math. Anal. 47 (2015), no. 1, 26–65.