| Issue |
E3S Web Conf.
Volume 609, 2025
The 7th International Conference on Multidiscipline Approaches for Sustainable Rural Development (ICMA SURE 2024)
|
|
|---|---|---|
| Article Number | 03003 | |
| Number of page(s) | 5 | |
| Section | Engineering and Technology | |
| DOI | https://doi.org/10.1051/e3sconf/202560903003 | |
| Published online | 24 January 2025 | |
Whole space case for solution formula of Korteweg type fluid motion in R3
1 Mathematics Department, Jenderal Soedirman University, Indonesia
2 International Islamic University, Malaysia
* Corresponding author: sri.maryani@unsoed.ac.id
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.
© The Authors, published by EDP Sciences, 2025
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