The aim of the Sino–Japan Conference of Young Mathematicians was to provide a forum for presenting and discussing recent trends and developments in differential equations and their applications, as well as to promote scientific exchanges and collaborations among young mathematicians both from China and Japan.The topics discussed in this proceedings include mean curvature flows, KAM theory, N-body problems, flows on Riemannian manifolds, hyperbolic systems, vortices, water waves, and reaction diffusion systems.Contents:A Spectral Theory of Linear Operators on Rigged Hilbert Spaces Under Certain Analyticity Conditions (H Chiba)Conditional Fredholm Determinant and Trace Formula for Hamiltonian Systems: A Survey (X-J Hu and P-H Wang)Initial Value Problem for Water Waves and Shallow Water and Long Wave Approximations (T Iguchi)On the Existence and Nonexistence of Maximizers Associated with Trudinger-Moser Type Inequalities in Unbounded Domains (M Ishiwata)Computer-Assisted Uniqueness Proof for Stokes' Wave of Extreme Form (K Kobayashi)From the Boltzmann H-Theorem to Perelman's W-Entropy Formula for the Ricci Flow (X-D Li)The Spreading of a New Species with Free Boundaries (X Liu and B Lou)Recent Progress on Observability for Stochastic Partial Differential Equations (Q Lü and Z-Q Yin)The Nonlinear “Hot Spots” Conjecture in Balls of S2 and H2 (Y Miyamoto)Mean-Field Models Describing Micro Phase Separation in the Two-Dimensional Case (B Niethammer and Y Oshita)Global Existence of Classical Solutions to Partially Dissipative Quasilinear Hyperbolic Systems (P Qu and C-M Liu)Time Averaged Properties Along Unstable Periodic Orbits of the Kuramoto-Sivashinsky Equation (Y Saiki and M Yamada)Anomalous Enstrophy Dissipation via the Self-Similar Triple Collapse of the Euler-α Point Vortices (T Sakajo)Action Minimizing Periodic Solutions in the N-Body Problem (M Shibayama)Some Geometric Problems of Conformally Compact Einstein Manifolds (Y Shi)Mathematical Modelling and Analysis of Droplet Motion on Obstacles (K Svadlenka)Introduction to Varifold and Its Curvature Flow (Y Tonegawa)Weak KAM Theory in Time-Periodic Lagrangian Systems (K-Z Wang and J Yan)A Note on Resonant Interaction of Rossby Waves in Two-Dimensional Flow on a β Plane (M Yamada and T Yoneda)Lp-Solvability of Nonlocal Parabolic Equations with Spatial Dependent and Non-Smooth Kernels (X-C Zhang)A Convergence Theorem of Kähler-Ricci Flow (Z-L Zhang)KP Approximation to the 3-D Water Wave Equations with Surface Tension (M Ming, P Zhang and Z-F Zhang)Smooth Convergence of Kähler-Ricci Flow on a Fano Manifold (X-H Zhu)Readership: Researchers and professionals in differential equations.