Weak Solution for 3D-Stochastic Third Grade Fluid Equations
This article studies the stochastic evolution of incompressible non-Newtonian fluids of differential type. More precisely, we consider the equations governing the dynamic of a third grade fluid filling a three-dimensional bounded domain <inline-formula><math display="inline">&l...
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| Format: | Article |
| Language: | English |
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MDPI AG
2020-11-01
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| Series: | Water |
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| Online Access: | https://www.mdpi.com/2073-4441/12/11/3211 |
| _version_ | 1797547710345117696 |
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| author | Adilson Almeida Fernanda Cipriano |
| author_facet | Adilson Almeida Fernanda Cipriano |
| author_sort | Adilson Almeida |
| collection | DOAJ |
| description | This article studies the stochastic evolution of incompressible non-Newtonian fluids of differential type. More precisely, we consider the equations governing the dynamic of a third grade fluid filling a three-dimensional bounded domain <inline-formula><math display="inline"><semantics><mi mathvariant="script">O</mi></semantics></math></inline-formula>, perturbed by a multiplicative white noise. Taking the initial condition in the Sobolev space <inline-formula><math display="inline"><semantics><mrow><msup><mi>H</mi><mn>2</mn></msup><mrow><mo stretchy="false">(</mo><mi mathvariant="script">O</mi><mo stretchy="false">)</mo></mrow></mrow></semantics></math></inline-formula>, and supplementing the equations with a Navier slip boundary condition, we establish the existence of a global weak stochastic solution with sample paths in <inline-formula><math display="inline"><semantics><mrow><msup><mi>L</mi><mo>∞</mo></msup><mrow><mo stretchy="false">(</mo><mn>0</mn><mo>,</mo><mi>T</mi><mo>;</mo><msup><mi>H</mi><mn>2</mn></msup><mrow><mo stretchy="false">(</mo><mi mathvariant="script">O</mi><mo stretchy="false">)</mo></mrow><mo stretchy="false">)</mo></mrow></mrow></semantics></math></inline-formula>. |
| first_indexed | 2024-03-10T14:49:04Z |
| format | Article |
| id | doaj.art-a598d5caba434e2781eaea5cc4f52100 |
| institution | Directory Open Access Journal |
| issn | 2073-4441 |
| language | English |
| last_indexed | 2024-03-10T14:49:04Z |
| publishDate | 2020-11-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Water |
| spelling | doaj.art-a598d5caba434e2781eaea5cc4f521002023-11-20T21:11:07ZengMDPI AGWater2073-44412020-11-011211321110.3390/w12113211Weak Solution for 3D-Stochastic Third Grade Fluid EquationsAdilson Almeida0Fernanda Cipriano1Faculdade de Ciências e Tecnologia da Universidade Nova de Lisboa and Centro de Matemática e Aplicações, Largo da Torre, 2825149 Caparica, PortugalFaculdade de Ciências e Tecnologia da Universidade Nova de Lisboa and Centro de Matemática e Aplicações, Largo da Torre, 2825149 Caparica, PortugalThis article studies the stochastic evolution of incompressible non-Newtonian fluids of differential type. More precisely, we consider the equations governing the dynamic of a third grade fluid filling a three-dimensional bounded domain <inline-formula><math display="inline"><semantics><mi mathvariant="script">O</mi></semantics></math></inline-formula>, perturbed by a multiplicative white noise. Taking the initial condition in the Sobolev space <inline-formula><math display="inline"><semantics><mrow><msup><mi>H</mi><mn>2</mn></msup><mrow><mo stretchy="false">(</mo><mi mathvariant="script">O</mi><mo stretchy="false">)</mo></mrow></mrow></semantics></math></inline-formula>, and supplementing the equations with a Navier slip boundary condition, we establish the existence of a global weak stochastic solution with sample paths in <inline-formula><math display="inline"><semantics><mrow><msup><mi>L</mi><mo>∞</mo></msup><mrow><mo stretchy="false">(</mo><mn>0</mn><mo>,</mo><mi>T</mi><mo>;</mo><msup><mi>H</mi><mn>2</mn></msup><mrow><mo stretchy="false">(</mo><mi mathvariant="script">O</mi><mo stretchy="false">)</mo></mrow><mo stretchy="false">)</mo></mrow></mrow></semantics></math></inline-formula>.https://www.mdpi.com/2073-4441/12/11/3211non-Newtonian fluidstochastic partial differential equationthird grade fluidturbulent flow |
| spellingShingle | Adilson Almeida Fernanda Cipriano Weak Solution for 3D-Stochastic Third Grade Fluid Equations Water non-Newtonian fluid stochastic partial differential equation third grade fluid turbulent flow |
| title | Weak Solution for 3D-Stochastic Third Grade Fluid Equations |
| title_full | Weak Solution for 3D-Stochastic Third Grade Fluid Equations |
| title_fullStr | Weak Solution for 3D-Stochastic Third Grade Fluid Equations |
| title_full_unstemmed | Weak Solution for 3D-Stochastic Third Grade Fluid Equations |
| title_short | Weak Solution for 3D-Stochastic Third Grade Fluid Equations |
| title_sort | weak solution for 3d stochastic third grade fluid equations |
| topic | non-Newtonian fluid stochastic partial differential equation third grade fluid turbulent flow |
| url | https://www.mdpi.com/2073-4441/12/11/3211 |
| work_keys_str_mv | AT adilsonalmeida weaksolutionfor3dstochasticthirdgradefluidequations AT fernandacipriano weaksolutionfor3dstochasticthirdgradefluidequations |