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Your search keyword '"Jolly, Michael S."' showing total 59 results
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59 results on '"Jolly, Michael S."'

52. Time analyticity with higher norm estimates for the 2D Navier-Stokes equations.

Author

FOIAS, CIPRIAN, JOLLY, MICHAEL S., LAN, RUOMENG, RUPAM, RISHIKA, YONG YANG, and BINGSHENG ZHANG

Subjects
*NAVIER-Stokes equations, *BOUNDARY value problems, *SET theory, *MATHEMATICS theorems, *APPLIED mathematics
Abstract

This paper establishes bounds on norms of all orders for solutions on the global attractor of the 2D Navier-Stokes equations, complexified in time. Specifically, for periodic boundary conditions on [0, L]2, and a force g ∈D(A(α-1)/2), we show that there is a fixed strip about the real-time axis on which a uniform bound [ABSTRACT FROM AUTHOR]

Published
2015
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58. Numerical Techniques for Approximating Lyapunov Exponents and Their Implementation

Author

Dieci, Luca, Jolly, Michael S., and Van Vleck, Erik S.

Abstract

The algorithms behind a toolbox for approximating Lyapunov exponents of nonlinear differential systems by QR methods are described. The basic solvers perform integration of the trajectory and approximation of the Lyapunov exponents simultaneously. That is, they integrate for the trajectory at the same time, and with the same underlying schemes, as is carried out for integration of the Lyapunov exponents. Separate computational procedures solve small systems for which the Jacobian matrix can be computed and stored, and for large systems for which the Jacobian cannot be stored, and may not even be explicitly known. If it is known, the user has the option to provide the action of the Jacobian on a vector. An alternative strategy is also presented in which one may want to approximate the trajectory with a specialized solver, linearize around the computed trajectory, and then carry out the approximation of the Lyapunov exponents using techniques for linear problems.

Published
2011
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59. Algebraic bounds on the Rayleigh–Bénard attractor

Author

Michael S. Jolly, Edriss S. Titi, Yu Cao, Jared P. Whitehead, Jolly, Michael S [0000-0002-7158-0933], Titi, Edriss S [0000-0002-5004-1746], Apollo - University of Cambridge Repository, Jolly, MS [0000-0002-7158-0933], and Titi, ES [0000-0002-5004-1746]

Subjects
Paper, General Mathematics, General Physics and Astronomy, global attractor, Enstrophy, 01 natural sciences, 76F35, Attractor, Periodic boundary conditions, Boundary value problem, 0101 mathematics, Algebraic number, Rayleigh–Bénard convection, math.AP, Mathematical Physics, Mathematics, Rayleigh-Benard convection, Plane (geometry), Applied Mathematics, 010102 general mathematics, Mathematical analysis, Statistical and Nonlinear Physics, 76E06, Nonlinear Sciences::Chaotic Dynamics, 010101 applied mathematics, 34D06, Homogeneous space, Affine space, synchronization, 35Q35
Abstract

Funder: John Simon Guggenheim Memorial Foundation; doi: https://doi.org/10.13039/100005851, Funder: Einstein Visiting Fellow Program, The Rayleigh–Bénard system with stress-free boundary conditions is shown to have a global attractor in each affine space where velocity has fixed spatial average. The physical problem is shown to be equivalent to one with periodic boundary conditions and certain symmetries. This enables a Gronwall estimate on enstrophy. That estimate is then used to bound the L 2 norm of the temperature gradient on the global attractor, which, in turn, is used to find a bounding region for the attractor in the enstrophy–palinstrophy plane. All final bounds are algebraic in the viscosity and thermal diffusivity, a significant improvement over previously established estimates. The sharpness of the bounds are tested with numerical simulations.

Published
2021
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