Fine Properties of Self-Similar Solutions of the Navier–Stokes Equations

By Lorenzo Brandolese. 2008

58 citations recorded by the source corpus.

We study the solutions of the nonstationary incompressible Navier–Stokes equations in $${\mathbb{R}^d}, d\geqq2$$, of self-similar form $${u(x,t)=\frac{1}{\sqrt t}U\left(\frac{x}{\sqrt t}\right)}$$, obtained from small and homogeneous initial data a(x). We construct an explicit asymptotic formula relating the self-similar profile U(x) of the velocity field to its corresponding initial datum a(x).

Subfields: Applied Mathematics, Computational Mechanics

View Paper: https://www.semanticscholar.org/paper/03b7e249b9cd44fa552b38fc4848c9ba37a4f73e

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Applied Mathematics

1. Maria E. Schonbek
2. Tai-Peng Tsai
3. Lorenzo Brandolese
4. Marco Cannone

In Computational Mechanics

1. Tai-Peng Tsai
2. Maria E. Schonbek
3. Lorenzo Brandolese

Citations in the corpus

• Large time decay and growth for solutions of a viscous Boussinesq system (2010, background): “t)(b−1)/2. Finally, since the mean of θremains constant in time, I1,1 j (x,t) = Z t 0 Kj,3(x,t−s) Z θ(y,s)dyds= Z θ0 Z Kj,3(x,t−s)ds. But the following decomposition of the kernel K, established in [7], holds : Kj,k(x,t) = Exj,x k (x) +|x|−3Ψj,k(x/ √ t), j,k= 1,2,3 where Ψj,k is fast decaying: |Ψ(y)”
• Forward Discretely Self-Similar Solutions of the Navier–Stokes Equations (2014, background): “Thus, K indeed maps bounded sets in X × [0, 1] into bounded sets in X .”