西北师范大学学报（自然科学版）2026，Vol.62Issue(1)：49-58,10.DOI:10.16783/j.cnki.nwnuz.2026.01.006
具有Dirichlet信号边界的趋化Navier-Stokes模型的整体适定性
Global well-posedness of a chemotaxis Navier-Stokes system involving Dirichlet boundary conditions for the signal
摘要
Abstract
The global well-posedness of a chemotaxis Navier-Stokes system involving quadratic decay and Dirichlet boundary conditions for the signal in a 2D bounded domain with smooth boundary is studied.To overcome the challenges posed by the non-homogeneous Dirichlet boundary conditions,the original problem is firstly transformed into the homogeneous Dirichlet boundary problem.Then,exploiting the local existence theory of solutions and the energy estimates,the global existence of uniformly bounded classical solutions is established for any suitably regular initial data.Moreover,the large-time behavior of the solution under certain additional assumptions is obtained via the Hölder estimates and the space-time estimates of solutions.关键词
趋化Navier-Stokes模型/Dirichlet信号边界条件/logistic源项/整体有界性/大时间行为Key words
chemotaxis Navier-Stokes system/Dirichlet boundary conditions for the signal/logistic source term/global boundedness/large-time behavior分类
数理科学引用本文复制引用
王晓琪,吴杰..具有Dirichlet信号边界的趋化Navier-Stokes模型的整体适定性[J].西北师范大学学报（自然科学版）,2026,62(1):49-58,10.基金项目
国家自然科学基金资助项目(12371201) （12371201）
