New results of general \(n\)-dimensional incompressible Navier-Stokes equations
The Cauchy problem for the general \(n\)-dimensional incompressible Navier-Stokes equations, with arbitrarily large initial data is considered in the whole space. The problem depends on a small parameter \(\varepsilon\), which multiplies the dispersion term. The paper deals with the exact limit of some \(L^2\)-norms of the global strong/weak solutions of the considered problem. For \(\varepsilon=0\), the mathematical analysis provided in this paper is formal and it is done in the sense of tempered distributions, while for \(\varepsilon>0\) the results are rigorous. By taking the initial data of a special form, the limits of physical quantities, as the time tends to \(\infty\), are established. These results suggest that after a long time, the solutions of the considered problem become closer and closer to the solutions of the linearized equation.
scientific article; zbMATH DE number 5382317
scientific article