Abstract
We consider the Cauchy problem for a multidimensional Burgers type equation with periodic boundary conditions. We obtain upper and lower bounds for derivatives of solutions for this equation in terms of powers of the viscosity and discuss how these estimates relate to the Kolmogorov-Obukhov spectral law. Next we use the estimates obtained to get certain bounds for derivatives of solutions of the Navier-Stokes system.
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Biryuk, A. (2004). On Multidimensional Burgers Type Equations with Small Viscosity. In: Galdi, G.P., Heywood, J.G., Rannacher, R. (eds) Contributions to Current Challenges in Mathematical Fluid Mechanics. Advances in Mathematical Fluid Mechanics. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-7877-7_1
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DOI: https://doi.org/10.1007/978-3-0348-7877-7_1
Publisher Name: Birkhäuser, Basel
Print ISBN: 978-3-0348-9606-1
Online ISBN: 978-3-0348-7877-7
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