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.
- density-dependent incompressible flow
- linearly growing data
ASJC Scopus subject areas
- Applied Mathematics