Domains of fractional powers of the Stokes operator in Lr spaces

1985 ◽  
Vol 89 (3) ◽  
pp. 251-265 ◽  
Author(s):  
Yoshikazu Giga
Keyword(s):  
Stokes Operator ◽  
Fractional Powers

Maximal Lp -Lq regularity to the Stokes problem with Navier boundary conditions

2017 ◽  
Vol 8 (1) ◽  
pp. 743-761 ◽  
Author(s):  
Hind Al Baba
Keyword(s):  
Boundary Conditions ◽  
Stress Tensor ◽  
Parabolic Problem ◽  
Stokes Problem ◽  
Stokes Operator ◽  
Fractional Powers ◽  
Navier Boundary Conditions ◽  
Regularity Results

Abstract We prove in this paper some results on the complex and fractional powers of the Stokes operator with slip frictionless boundary conditions involving the stress tensor. This is fundamental and plays an important role in the associated parabolic problem and will be used to prove maximal L^{p} - L^{q} regularity results for the non-homogeneous Stokes problem.

scholarly journals On Fractional Powers of the Stokes Operator

1970 ◽  
Vol 46 (10Supplement) ◽  
pp. 1141-1143
Author(s):  
Hiroshi FUJITA ◽  
Hiroko MORIMOTO
Keyword(s):  
Stokes Operator ◽  
Fractional Powers

scholarly journals On fractional powers of the Stokes operator

1970 ◽  
Vol 46 ◽  
pp. 1141-1143 ◽  
Author(s):  
Hiroshi Fujita ◽  
Hiroko Morimoto
Keyword(s):  
Stokes Operator ◽  
Fractional Powers

scholarly journals Rational Krylov methods for fractional diffusion problems on graphs

2021 ◽  
Author(s):  
Michele Benzi ◽  
Igor Simunec
Keyword(s):  
Analytic Function ◽  
Diffusion Equation ◽  
Graph Laplacian ◽  
Fractional Diffusion ◽  
Singular Matrix ◽  
Krylov Methods ◽  
Fractional Powers ◽  
Directed Networks ◽  
Rank One ◽  
Diffusion Problems

AbstractIn this paper we propose a method to compute the solution to the fractional diffusion equation on directed networks, which can be expressed in terms of the graph Laplacian L as a product $$f(L^T) \varvec{b}$$ f ( L T ) b , where f is a non-analytic function involving fractional powers and $$\varvec{b}$$ b is a given vector. The graph Laplacian is a singular matrix, causing Krylov methods for $$f(L^T) \varvec{b}$$ f ( L T ) b to converge more slowly. In order to overcome this difficulty and achieve faster convergence, we use rational Krylov methods applied to a desingularized version of the graph Laplacian, obtained with either a rank-one shift or a projection on a subspace.

scholarly journals Unitarity of theories containing fractional powers of the d’Alembertian operator

2014 ◽  
Vol 90 (10) ◽  
Author(s):  
E. C. Marino ◽  
Leandro O. Nascimento ◽  
Van Sérgio Alves ◽  
C. Morais Smith
Keyword(s):  
Fractional Powers
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