Aims. The filamentary ~10-pc-scale infrared dark cloud L1287 located at a parallax distance of ~929 pc is actively forming a dense cluster of low-mass young stellar objects (YSOs) at its inner ~0.1 pc region. To help understand the origin of this low-mass YSO cluster, the present work aims at resolving the gas structures and kinematics with high angular resolution. Methods. We performed ~1′′ angular resolution (~930 AU) observations at ~1.3 mm wavelengths using the Submillimeter Array (SMA), which simultaneously cover the dust continuum emission and various molecular line tracers for dense gas, warm gas, shocks, and outflows. Results. From a 1.3-mm continuum image with a resolution of ~2′′ we identified six dense cores, namely SMA1-6. Their gas masses are in the range of ~0.4–4 M_⊙. From a 1.3-mm continuum image with a resolution of ~1′′, we find a high fragmentation level, with 14 compact millimeter sources within 0.1 pc: SMA3 contains at least nine internal condensations; SMA5 and SMA6 are also resolved with two internal condensations. Intriguingly, one condensation in SMA3 and another in SMA5 appear associated with the known accretion outburst YSOs RNO 1C and RNO 1B. The dense gas tracer DCN (3–2) well traces the dust continuum emission and shows a clear velocity gradient along the NW-SE direction centered at SMA3. There is another velocity gradient with opposite direction around the most luminous YSO, IRAS 00338 + 6312. Conclusions. The fragmentation within 0.1 pc in L1287 is very high compared to other regions at the same spatial scales. The incoherent motions of dense gas flows are sometimes interpreted by being influenced by (proto)stellar feedback (e.g., outflows), which is not yet ruled out in this particular target source. On the other hand, the velocities (with respect to the systemic velocity) traced by DCN are small, and the directions of the velocity gradients traced by DCN are approximately perpendicular to those of the dominant CO outflow(s). Therefore, we alternatively hypothesize that the velocity gradients revealed by DCN trace the convergence from the ≳0.1 pc scales infalling motion towards the rotational motions around the more compact (~0.02 pc) sources. This global molecular gas converging flow may feed the formation of the dense low-mass YSO cluster. Finally, we also found that IRAS 00338 + 6312 is the most likely powering source of the dominant CO outflow. A compact blue-shifted outflow from RNO 1C is also identified.