Skip to main content

PDEs and Fluid Dynamics

  • 2493 Accesses

Part of the Lecture Notes in Mathematics book series (LNM,volume 2017)

Abstract

We use the theory of Calderón–Zygmund operators to prove regularity results for the Poisson problem and the Stokes problem, to show the solvability of the divergence equation, and to prove Korn’s inequality. These problems belong to the most classical problems treated in the theory of partial differential equations and fluid dynamics. It turns out that the treatment, especially of the whole space problems requires the notion of homogeneous Sobolev spaces, which have been studied in Sect. 12.2. The Poisson problem and the Stokes system are studied in the first two sections. After that we study the divergence equation and its consequences.

Keywords

  • Divergence Equation
  • Stokes Problem
  • Variable Exponent
  • Newton Potential
  • Unique Strong Solution

These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

This is a preview of subscription content, access via your institution.

Buying options

Chapter
USD   29.95
Price excludes VAT (Canada)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD   79.99
Price excludes VAT (Canada)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD   99.99
Price excludes VAT (Canada)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Learn about institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Lars Diening .

Rights and permissions

Reprints and Permissions

Copyright information

© 2011 Springer-Verlag Berlin Heidelberg

About this chapter

Cite this chapter

Diening, L., Harjulehto, P., Hästö, P., Růžička, M. (2011). PDEs and Fluid Dynamics. In: Lebesgue and Sobolev Spaces with Variable Exponents. Lecture Notes in Mathematics(), vol 2017. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-18363-8_14

Download citation