arXiv subjects

Lineia Schutz

Publications and source records attributed to Lineia Schutz.

3 recordsLinked to original sources

arXiv2018

On the supnorm form of Leray's problem for the incompressible Navier-Stokes equations

We show that t^{3/4}|| u(.,t) ||_{sup} --> 0 as t --> infty for all (global) Leray solutions of the incompressible Navier-Stokes equations in R3. It is also shown that t || u(.,t) - v(.,t) ||_{sup} --> 0 as t --> infty, where v(.,t) is the Stokes approximation, as well as other fundamental results. In spite of the difficulty of these questions, our approach is elementary and is based on standard tools like conventional Fourier and energy methods.

math.AP↗

arXiv2016

Sharp pointwise estimates for functions in the Sobolev spaces Hs(Rn)

We obtain the optimal value of the constant K(n,s) in the Sobolev-Nirenberg-Gagliardo inequality $ \|\,u\,\|_{L^{\infty}(\mathbb{R}^{n})} \leq K(n,s) \,\|\, u \,\|_{L^{2}(\mathbb{R}^{n})}^{1 - n/(2s)} \|\, u \,\|_{\dot{H}^{s}(\mathbb{R}^{n})}^{n/(2s)} $ where $ s > n/2 $.

math.FA↗

arXiv2015

On the Blow-up Criterion of Magnetohydrodynamics Equations in Homogeneous Sobolev Spaces

In this paper, we obtain new lower bounds on the Homogeneous Sobolev--norms of the maximal solution of the Magnetohydrodynamics Equations. This gives us some insight on the blow-up behavior of the solution. We utilize standard techniques from the Navier--Stokes Equations.

math.AP↗