Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely:  construct wavelet Riesz bases for the usual Sobolev spaces of divergence free functions on that have vanishing normals at the boundary.  give a simultaneous space-time variational formulation of the instationary Stokes equations that defines a boundedly invertible mapping beten a Bochner space and the dual of another Bochner space. By equipping these Bochner spaces by tensor products of temporal and divergence-free spatial wavelets, the Stokes problem is rewritten as an equivalent ll-posed bi-infinite matrix vector equation. This equation can be solved with an adaptive wavelet method in linear complexity with best possible rate, that, under some mild Besov smoothness conditions, is nearly independent of the space dimension. For proving one of the intermediate results,  construct an eigenfunction basis of the stationary Stokes operator.
['Rob Stevenson']
I am writing a research paper on a idea Divergence-free wavelet bases on the hypercube: free-slip boundary conditions, and applications for solving the instationary Stokes equations
[{"from": "human", "value": "I am writing a research paper on a idea Divergence-free wavelet bases on the hypercube: free-slip boundary conditions, and applications for solving the instationary Stokes equations"}, {"from": "gpt", "value": "Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely:  construct wavelet Riesz bases for the usual Sobolev spaces of divergence free functions on that have vanishing normals at the boundary.  give a simultaneous space-time variational formulation of the instationary Stokes equations that defines a boundedly invertible mapping beten a Bochner space and the dual of another Bochner space. By equipping these Bochner spaces by tensor products of temporal and divergence-free spatial wavelets, the Stokes problem is rewritten as an equivalent ll-posed bi-infinite matrix vector equation. This equation can be solved with an adaptive wavelet method in linear complexity with best possible rate, that, under some mild Besov smoothness conditions, is nearly independent of the space dimension. For proving one of the intermediate results,  construct an eigenfunction basis of the stationary Stokes operator."}]