Density-dependent incompressible viscous fluid flow subject to linearly growing initial data

Abstract

Consider the density-dependent incompressible Navier–Stokes equations in ℝ ^N with linearly growing initial data at infinity. It is shown that under certain regularity and growth assumptions on the data, the above system admits a unique, local solution. Moreover, the solution can be extended for arbitrary T > 0, provided the data are small enough with respect to a certain norm

Keywords:

• density-dependent incompressible flow
• Navier–Stokes
• linearly growing data
• paraproducts

AMS Subject Classifications::

• 35Q30
• 35Q35
• 76D03

Acknowledgements

Part of this work was done while D.Y. Fang and T. Zhang were visiting Fachbereich Mathematik, Technische Universität Darmstadt, in October 2010, supported by the project ‘Analysis of PDE and applications‘ (NSFC of China and DFG of Germany). They appreciate the hospitality from Technische Universität Darmstadt. They were supported in part by the NSFC of China (10871175, 10931007, 10901137), Zhejiang Provincial Natural Science Foundation of China Z6100217 and SRFDP No. 20090101120005.