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- W4387074397 abstract "The following convective Brinkman-Forchheimer (CBF) equations (or damped Navier-Stokes equations) with potential$ begin{equation*} frac{partial boldsymbol{y}}{partial t}-mu Deltaboldsymbol{y}+(boldsymbol{y}cdotnabla)boldsymbol{y}+alphaboldsymbol{y}+beta|boldsymbol{y}|^{r-1}boldsymbol{y}+nabla p+Psi(boldsymbol{y})niboldsymbol{g}, nablacdotboldsymbol{y} = 0, end{equation*} $in a $ d $-dimensional torus is considered in this work, where $ din{2,3} $, $ mu,alpha,beta>0 $ and $ rin[1,infty) $. For $ d = 2 $ with $ rin[1,infty) $ and $ d = 3 $ with $ rin[3,infty) $ ($ 2betamugeq 1 $ for $ d = r = 3 $), we establish the existence of a unique global strong solution for the above multi-valued problem with the help of the abstract theory of $ m $-accretive operators. Moreover, we demonstrate that the same results hold local in time for the case $ d = 3 $ with $ rin[1,3) $ and $ d = r = 3 $ with $ 2betamu<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 $ rin[1,3] $, we quantize (modify) the Navier-Stokes nonlinearity $ (boldsymbol{y}cdotnabla)boldsymbol{y} $ to establish the existence and uniqueness results, while for $ rin[3,infty) $ ($ 2betamugeq1 $ for $ r = 3 $), we handle the Navier-Stokes nonlinearity by the nonlinear damping term $ beta|boldsymbol{y}|^{r-1}boldsymbol{y} $. Finally, we discuss the applications of the above developed theory in feedback control problems like flow invariance, time optimal control and stabilization." @default.
- W4387074397 created "2023-09-27" @default.
- W4387074397 creator A5031256718 @default.
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- W4387074397 date "2023-01-01" @default.
- W4387074397 modified "2023-10-17" @default.
- W4387074397 title "2D and 3D convective Brinkman-Forchheimer equations perturbed by a subdifferential and applications to control problems" @default.
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- W4387074397 doi "https://doi.org/10.3934/mcrf.2023034" @default.
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