Cauchy convergence schemes for some nonlinear partial differential equations
نویسنده
چکیده
Motivated by ongoing work in the theory of stochastic partial differential equations we develop direct methods to infer that the Galerkin approximations of certain nonlinear partial differential equations are Cauchy (and therefore convergent). We develop such a result for the Navier–Stokes equations in space dimensions two and three, and for the primitive equations in space dimension two. The analysis requires novel estimates for the nonlinear portion of these equations and delicate interpolation results concerning subspaces.
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