2D and 3D convective Brinkman-Forchheimer equations perturbed by a subdifferential and applications to control problems Article Swipe
Sagar Gautam
,
Kush Kinra
,
Manil T. Mohan
·
YOU?
·
· 2023
· Open Access
·
· DOI: https://doi.org/10.3934/mcrf.2023034
YOU?
·
· 2023
· Open Access
·
· DOI: https://doi.org/10.3934/mcrf.2023034
The following convective Brinkman-Forchheimer (CBF) equations (or damped Navier-Stokes equations) with potential$ \begin{equation*} \frac{\partial \boldsymbol{y}}{\partial t}-\mu \Delta\boldsymbol{y}+(\boldsymbol{y}\cdot\nabla)\boldsymbol{y}+\alpha\boldsymbol{y}+\beta|\boldsymbol{y}|^{r-1}\boldsymbol{y}+\nabla p+\Psi(\boldsymbol{y})\ni\boldsymbol{g},\ \nabla\cdot\boldsymbol{y} = 0, \end{equation*} $in a $ d $-dimensional torus is considered in this work, where $ d\in\{2,3\} $, $ \mu,\alpha,\beta>0 $ and $ r\in[1,\infty) $. For $ d = 2 $ with $ r\in[1,\infty) $ and $ d = 3 $ with $ r\in[3,\infty) $ ($ 2\beta\mu\geq 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 $ r\in[1,3) $ and $ d = r = 3 $ with $ 2\beta\mu<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\in[1,3] $, we quantize (modify) the Navier-Stokes nonlinearity $ (\boldsymbol{y}\cdot\nabla)\boldsymbol{y} $ to establish the existence and uniqueness results, while for $ r\in[3,\infty) $ ($ 2\beta\mu\geq1 $ 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.
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- en
- Landing Page
- https://doi.org/10.3934/mcrf.2023034
- https://www.aimsciences.org/data/article/export-pdf?id=6511447520e8085b32241104
- OA Status
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- Cited By
- 1
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- Related Works
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- DOI
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https://doi.org/10.3934/mcrf.2023034Digital Object Identifier
- Title
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2D and 3D convective Brinkman-Forchheimer equations perturbed by a subdifferential and applications to control problemsWork title
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articleOpenAlex work type
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enPrimary language
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2023Year of publication
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2023-09-26Full publication date if available
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Sagar Gautam, Kush Kinra, Manil T. MohanList of authors in order
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https://doi.org/10.3934/mcrf.2023034Publisher landing page
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https://www.aimsciences.org/data/article/export-pdf?id=6511447520e8085b32241104Direct link to full text PDF
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Nabla symbol, Uniqueness, Physics, Order (exchange), Combinatorics, Navier–Stokes equations, Mathematical physics, Mathematics, Mathematical analysis, Omega, Quantum mechanics, Thermodynamics, Compressibility, Finance, EconomicsTop concepts (fields/topics) attached by OpenAlex
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| abstract_inverted_index.a | 23, 81 |
| abstract_inverted_index.d | 25, 46, 56, 70, 118, 128 |
| abstract_inverted_index.m | 100, 142 |
| abstract_inverted_index.r | 72, 130, 196 |
| abstract_inverted_index.$, | 36, 169 |
| abstract_inverted_index.$. | 43, 137, 212 |
| abstract_inverted_index.($ | 64, 191 |
| abstract_inverted_index.0, | 20 |
| abstract_inverted_index.We | 138 |
| abstract_inverted_index.as | 147, 149 |
| abstract_inverted_index.by | 205 |
| abstract_inverted_index.in | 30, 112, 163, 223 |
| abstract_inverted_index.is | 28 |
| abstract_inverted_index.of | 80, 94, 98, 144, 218 |
| abstract_inverted_index.to | 179 |
| abstract_inverted_index.we | 76, 104, 170, 200, 214 |
| abstract_inverted_index.$), | 75, 199 |
| abstract_inverted_index.$in | 22 |
| abstract_inverted_index.(or | 6 |
| abstract_inverted_index.For | 44, 166 |
| abstract_inverted_index.The | 0 |
| abstract_inverted_index.and | 40, 54, 126, 154, 157, 183, 233 |
| abstract_inverted_index.for | 68, 86, 114, 187, 194 |
| abstract_inverted_index.the | 78, 87, 92, 95, 107, 115, 140, 145, 164, 173, 181, 202, 206, 216, 219 |
| abstract_inverted_index.case | 116 |
| abstract_inverted_index.flow | 228 |
| abstract_inverted_index.help | 93 |
| abstract_inverted_index.hold | 110 |
| abstract_inverted_index.like | 227 |
| abstract_inverted_index.same | 108 |
| abstract_inverted_index.term | 209 |
| abstract_inverted_index.that | 106 |
| abstract_inverted_index.this | 31 |
| abstract_inverted_index.time | 113, 230 |
| abstract_inverted_index.well | 148 |
| abstract_inverted_index.with | 10, 50, 60, 91, 122, 134 |
| abstract_inverted_index.(CBF) | 4 |
| abstract_inverted_index.above | 88, 220 |
| abstract_inverted_index.local | 111 |
| abstract_inverted_index.order | 160 |
| abstract_inverted_index.their | 155 |
| abstract_inverted_index.torus | 27 |
| abstract_inverted_index.where | 33 |
| abstract_inverted_index.while | 186 |
| abstract_inverted_index.work, | 32 |
| abstract_inverted_index.Yosida | 152 |
| abstract_inverted_index.damped | 7 |
| abstract_inverted_index.energy | 161 |
| abstract_inverted_index.global | 83 |
| abstract_inverted_index.handle | 201 |
| abstract_inverted_index.higher | 159 |
| abstract_inverted_index.strong | 84 |
| abstract_inverted_index.theory | 97, 222 |
| abstract_inverted_index.t}-\mu | 15 |
| abstract_inverted_index.unique | 82 |
| abstract_inverted_index.control | 225, 232 |
| abstract_inverted_index.damping | 208 |
| abstract_inverted_index.discuss | 215 |
| abstract_inverted_index.optimal | 231 |
| abstract_inverted_index.problem | 90 |
| abstract_inverted_index.proofs. | 165 |
| abstract_inverted_index.results | 109 |
| abstract_inverted_index.several | 158 |
| abstract_inverted_index.(modify) | 172 |
| abstract_inverted_index.Finally, | 213 |
| abstract_inverted_index.abstract | 96 |
| abstract_inverted_index.explored | 139 |
| abstract_inverted_index.feedback | 224 |
| abstract_inverted_index.problems | 226 |
| abstract_inverted_index.quantize | 171 |
| abstract_inverted_index.results, | 185 |
| abstract_inverted_index.solution | 85 |
| abstract_inverted_index.Moreover, | 103 |
| abstract_inverted_index.developed | 221 |
| abstract_inverted_index.equations | 5 |
| abstract_inverted_index.establish | 77, 180 |
| abstract_inverted_index.estimates | 162 |
| abstract_inverted_index.existence | 79, 182 |
| abstract_inverted_index.following | 1 |
| abstract_inverted_index.nonlinear | 146, 207 |
| abstract_inverted_index.r\in[1,3) | 124 |
| abstract_inverted_index.r\in[1,3] | 168 |
| abstract_inverted_index.considered | 29 |
| abstract_inverted_index.convective | 2 |
| abstract_inverted_index.equations) | 9 |
| abstract_inverted_index.operators, | 151 |
| abstract_inverted_index.operators. | 102 |
| abstract_inverted_index.potential$ | 11 |
| abstract_inverted_index.uniqueness | 184 |
| abstract_inverted_index.$-accretive | 101 |
| abstract_inverted_index.2\beta\mu<1 | 136 |
| abstract_inverted_index.d\in\{2,3\} | 35 |
| abstract_inverted_index.demonstrate | 105 |
| abstract_inverted_index.invariance, | 229 |
| abstract_inverted_index.properties, | 156 |
| abstract_inverted_index.applications | 217 |
| abstract_inverted_index.multi-valued | 89, 150 |
| abstract_inverted_index.nonlinearity | 175, 204 |
| abstract_inverted_index.$-accretivity | 143 |
| abstract_inverted_index.$-dimensional | 26 |
| abstract_inverted_index.2\beta\mu\geq | 65 |
| abstract_inverted_index.Navier-Stokes | 8, 174, 203 |
| abstract_inverted_index.2\beta\mu\geq1 | 192 |
| abstract_inverted_index.\frac{\partial | 13 |
| abstract_inverted_index.approximations | 153 |
| abstract_inverted_index.r\in[1,\infty) | 42, 52 |
| abstract_inverted_index.r\in[3,\infty) | 62, 189 |
| abstract_inverted_index.stabilization. | 234 |
| abstract_inverted_index.\end{equation*} | 21 |
| abstract_inverted_index.\begin{equation*} | 12 |
| abstract_inverted_index.\mu,\alpha,\beta>0 | 38 |
| abstract_inverted_index.Brinkman-Forchheimer | 3 |
| abstract_inverted_index.\boldsymbol{y}}{\partial | 14 |
| abstract_inverted_index.\nabla\cdot\boldsymbol{y} | 18 |
| abstract_inverted_index.(\boldsymbol{y}\cdot\nabla)\boldsymbol{y} | 177 |
| abstract_inverted_index.\beta|\boldsymbol{y}|^{r-1}\boldsymbol{y} | 211 |
| abstract_inverted_index.p+\Psi(\boldsymbol{y})\ni\boldsymbol{g},\ | 17 |
| abstract_inverted_index.\Delta\boldsymbol{y}+(\boldsymbol{y}\cdot\nabla)\boldsymbol{y}+\alpha\boldsymbol{y}+\beta|\boldsymbol{y}|^{r-1}\boldsymbol{y}+\nabla | 16 |
| cited_by_percentile_year.max | 95 |
| cited_by_percentile_year.min | 91 |
| countries_distinct_count | 1 |
| institutions_distinct_count | 3 |
| citation_normalized_percentile.value | 0.65189873 |
| citation_normalized_percentile.is_in_top_1_percent | False |
| citation_normalized_percentile.is_in_top_10_percent | False |