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Published in:
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2004 | OriginalPaper | Chapter

On Multidimensional Burgers Type Equations with Small Viscosity

Author : Andrei Biryuk

Published in: Contributions to Current Challenges in Mathematical Fluid Mechanics

Publisher: Birkhäuser Basel

Included in: Professional Book Archive

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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.

next chapter On the Global Well-posedness and Stability of the Navier—Stokes and the Related Equations
Metadata
Title
On Multidimensional Burgers Type Equations with Small Viscosity
Author
Andrei Biryuk
Copyright Year
2004
Publisher
Birkhäuser Basel
Book
Contributions to Current Challenges in Mathematical Fluid Mechanics

Print ISBN: 978-3-0348-9606-1

Electronic ISBN: 978-3-0348-7877-7

Copyright Year: 2004

DOI
https://doi.org/10.1007/978-3-0348-7877-7_1

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