Whole space case for solution formula of Korteweg type fluid motion in R3
In this paper we consider the solution formula of linearized diffusive capillary model of Korteweg type without surface tension in three-dimensional Euclidean space ℝ3 using Fourier transform. Firstly, we construct the matrix of differential operators from the model problem. Then, we apply Fourier t...
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| Main Authors: | , , , , , |
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| Format: | Article |
| Language: | English |
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EDP Sciences
2025-01-01
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| Series: | E3S Web of Conferences |
| Online Access: | https://www.e3s-conferences.org/articles/e3sconf/pdf/2025/09/e3sconf_icma-sure2024_03003.pdf |
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| author | Bagus Suhada Dede Maryani Sri Renny Renny Triyani Triyani Hendriya Guswanto Bambang Kartiwi Mira |
| author_facet | Bagus Suhada Dede Maryani Sri Renny Renny Triyani Triyani Hendriya Guswanto Bambang Kartiwi Mira |
| author_sort | Bagus Suhada Dede |
| collection | DOAJ |
| description | In this paper we consider the solution formula of linearized diffusive capillary model of Korteweg type without surface tension in three-dimensional Euclidean space ℝ3 using Fourier transform. Firstly, we construct the matrix of differential operators from the model problem. Then, we apply Fourier transform to the matrix. In the third step, we consider the resolvent problem of model problem. Finally, we find the solution formula of velocity and density by using inverse Fourier transform. For the further research we can consider not only estimating the solution operator families of the Korteweg theory of capillarity but also estimating the optimal decay for solution to the non-linear problem. |
| format | Article |
| id | doaj-art-206b65dc509b4530869ff4cf900ea3a2 |
| institution | Kabale University |
| issn | 2267-1242 |
| language | English |
| publishDate | 2025-01-01 |
| publisher | EDP Sciences |
| record_format | Article |
| series | E3S Web of Conferences |
| spelling | doaj-art-206b65dc509b4530869ff4cf900ea3a22025-02-05T10:49:56ZengEDP SciencesE3S Web of Conferences2267-12422025-01-016090300310.1051/e3sconf/202560903003e3sconf_icma-sure2024_03003Whole space case for solution formula of Korteweg type fluid motion in R3Bagus Suhada Dede0Maryani Sri1Renny Renny2Triyani Triyani3Hendriya Guswanto Bambang4Kartiwi Mira5Mathematics Department, Jenderal Soedirman UniversityMathematics Department, Jenderal Soedirman UniversityMathematics Department, Jenderal Soedirman UniversityMathematics Department, Jenderal Soedirman UniversityMathematics Department, Jenderal Soedirman UniversityInternational Islamic UniversityIn this paper we consider the solution formula of linearized diffusive capillary model of Korteweg type without surface tension in three-dimensional Euclidean space ℝ3 using Fourier transform. Firstly, we construct the matrix of differential operators from the model problem. Then, we apply Fourier transform to the matrix. In the third step, we consider the resolvent problem of model problem. Finally, we find the solution formula of velocity and density by using inverse Fourier transform. For the further research we can consider not only estimating the solution operator families of the Korteweg theory of capillarity but also estimating the optimal decay for solution to the non-linear problem.https://www.e3s-conferences.org/articles/e3sconf/pdf/2025/09/e3sconf_icma-sure2024_03003.pdf |
| spellingShingle | Bagus Suhada Dede Maryani Sri Renny Renny Triyani Triyani Hendriya Guswanto Bambang Kartiwi Mira Whole space case for solution formula of Korteweg type fluid motion in R3 E3S Web of Conferences |
| title | Whole space case for solution formula of Korteweg type fluid motion in R3 |
| title_full | Whole space case for solution formula of Korteweg type fluid motion in R3 |
| title_fullStr | Whole space case for solution formula of Korteweg type fluid motion in R3 |
| title_full_unstemmed | Whole space case for solution formula of Korteweg type fluid motion in R3 |
| title_short | Whole space case for solution formula of Korteweg type fluid motion in R3 |
| title_sort | whole space case for solution formula of korteweg type fluid motion in r3 |
| url | https://www.e3s-conferences.org/articles/e3sconf/pdf/2025/09/e3sconf_icma-sure2024_03003.pdf |
| work_keys_str_mv | AT bagussuhadadede wholespacecaseforsolutionformulaofkortewegtypefluidmotioninr3 AT maryanisri wholespacecaseforsolutionformulaofkortewegtypefluidmotioninr3 AT rennyrenny wholespacecaseforsolutionformulaofkortewegtypefluidmotioninr3 AT triyanitriyani wholespacecaseforsolutionformulaofkortewegtypefluidmotioninr3 AT hendriyaguswantobambang wholespacecaseforsolutionformulaofkortewegtypefluidmotioninr3 AT kartiwimira wholespacecaseforsolutionformulaofkortewegtypefluidmotioninr3 |