The　goal　of　community　search　is　to　provide　effective　solutions　for　real-time,　high-quality　community　searches　within　large　networks.　In　many　practical　applications,　such　as　event　organization　and　friend　recommendations,　discovering　various　community　structures　within　a　network　is　crucial　for　users.　However,　existing　community　search　algorithms　rarely　address　issues　within　temporal　graphs,　and　those　that　do　often　have　two　main　limitations:　(1)　traditional　community　search　methods　become　inefficient　and　experience　significant　increases　in　computation　time　when　scaled　to　large　graphs;　(2)　while　GNN-based　community　search　methods　for　temporal　graphs　offer　generalizability,　they　often　focus　solely　on　community　connectivity　and　lack　cohesiveness.　Therefore,　we　propose　a　new　model　PK-GCN,　based　on　Graph　Neural　Networks　(GNNs),　to　identify　persistent　k-core　communities　in　temporal　networks.　This　model　can　handle　dynamic　changes　in　temporal　graphs　and　identify　communities　that　persist　over　time.　Compared　to　existing　community　search　methods,　our　model　not　only　finds　communities　with　tighter　structures　but　also　allows　for　dynamic　queries　based　on　user　input　without　needing　retraining.　Specifically,　our　model　constructs　features　by　integrating　k-core　information　from　core　decomposition,　graph　features,　and　query　features,　resulting　in　more　expressive　node　representations.　Additionally,　we　designed　a　flexible　dynamic　query　mechanism　that　allows　users　to　input　time　information　to　query　communities.　Experiments　on　multiple　datasets　demonstrate　that　our　model　outperforms　other　GNN-based　community　search　algorithms　in　F1-score.　©　2024　IEEE.