On the constants in a basic inequality for the Euler and Navier-Stokes equations

Details On the constants in a basic inequality for the Euler and Navier-Stokes equations On the constants in a basic inequality for the Euler and Navier-Stokes equations

2010-07-26

arxiv.org/abs/1007.4412v2

Mathematics

Analysis of PDEs

LaTeX, 36 pages. A few style changes, some references added

Scientific paper

We consider the incompressible Euler or Navier-Stokes (NS) equations on a d-dimensional torus T^d; the quadratic term in these equations arises from the bilinear map sending two velocity fields v, w : T^d -> R^d into v . D w, and also involves the Leray projection L onto the space of divergence free vector fields. We derive upper and lower bounds for the constants in some inequalities related to the above quadratic term; these bounds hold, in particular, for the sharp constants K_{n d} = K_n in the basic inequality || L(v . D w)||_n <= K_n || v ||_n || w ||_{n+1}, where n in (d/2, + infinity) and v, w are in the Sobolev spaces H^n, H^{n+1} of zero mean, divergence free vector fields of orders n and n+1, respectively. As examples, the numerical values of our upper and lower bounds are reported for d=3 and some values of n. Some practical motivations are indicated for an accurate analysis of the constants K_n.

Affiliated with

Also associated with

No associations

Rating

On the constants in a basic inequality for the Euler and Navier-Stokes equations does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with On the constants in a basic inequality for the Euler and Navier-Stokes equations, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and On the constants in a basic inequality for the Euler and Navier-Stokes equations will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-558635