A simple proof of global solvability of 2-D Navier-Stokes equations in unbounded domains

Fernando, B. P. W.; Sritharan, S. S.; Xu, Meng

doi:10.57262/die/1356019315

Cited by 5 publications

(1 citation statement)

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“…The theory of monotone operators is an important tool in the study of nonlinear operator equations, we refer the readers to [5,6,19,31,39], etc., for more details. When the operator has some kind of monotonicity properties, then one can pass to the limit in the Galerkin and Faedo-Galerkin approximations of the original equation, with a-priori estimates that are in general weaker than those necessary in the compactness methods (see [22]). In particular, monotone operators are suitable tools for studying variational inequalities (see [6]).…”

Section: Introductionmentioning

confidence: 99%

2D and 3D convective Brinkman-Forchheimer equations perturbed by a subdifferential and applications to control problems

Gautam,

Kinra,

Mohan

2024

MCRF

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The following convective Brinkman-Forchheimer (CBF) equations (or damped Navier-Stokes equations) with potential), we establish the existence of a unique global strong solution for the above multi-valued problem with the help of the abstract theory of maccretive operators. Moreover, we demonstrate that the same results hold local in time for the case d = 3 with r ∈ [1, 3) and d = r = 3 with 2βµ < 1. We explored the m-accretivity of the nonlinear as well as multi-valued operators, Yosida approximations and their properties, and several higher order energy estimates in the proofs. For r ∈ [1, 3], we quantize (modify) the Navier-Stokes nonlinearity (y • ∇)y to establish the existence and uniqueness results, while for r ∈ [3, ∞) (2βµ ≥ 1 for r = 3), we handle the Navier-Stokes nonlinearity by the nonlinear damping term β|y| r−1 y. Finally, we discuss the applications of the above developed theory in feedback control problems like flow invariance, time optimal control and stabilization.

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