Whole space case for solution formula of Korteweg type fluid motion in R3 - Bagus Suhada Dede; Maryani Sri; Renny Renny; Triyani Triyani; Hendriya Guswanto Bambang; Kartiwi Mira (E3S Web of Conferences)
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.