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Existence and uniqueness of solutions for a modified Navier-Stokes equation in $$\mathbb{R}^2$$. (English) Zbl 0893.35093
The author establishes existence and uniqueness of solutions $$v(t,x)=(v_{1}(t,x),v_{2}(t,x))$$ and $$p(t,x)$$, $$x\in \mathbb{R}^{2}$$ and $$0\leq t\leq T<\infty$$ to the Navier-Stokes equations with hyperdissipation. This means that the Laplacian, responsible for dissipating energy from the system, is replaced by a higher order dissipation mechanism which damps the high wave numbers more selectively. The choice made by the author is the operator $$L=-(-\Delta ^d)$$ for some $$d\geq 1$$. This modification allows more affordable numerical simulations of turbulent flows.
Reviewer: F.Rosso (Firenze)

##### MSC:
 35Q30 Navier-Stokes equations 76D05 Navier-Stokes equations for incompressible viscous fluids
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