Strong Solutions for the Stochastic Cahn-Hilliard Convective Brinkman-Forchheimer Model for Tumor Growth
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2026
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| author | Rawat, Kalpana Sakthivel, Kumarasamy |
| author_facet | Rawat, Kalpana Sakthivel, Kumarasamy |
| contents | In this work, we analyze a diffuse-interface model for tumor growth, subject to multiplicative white noises, posed on a bounded domain $\mathcal{O} \subset \mathbb{R}^d$, $d=2,3$. The model couples a stochastic incompressible convective Brinkman-Forchheimer (CBF) equation or Navier-Stokes equation with damping $η|v|^{r-1}v $ for the averaged velocity field $v$, to a Cahn-Hilliard (CH) equation for the phase field variable $ϕ$ and to a stochastic reaction-diffusion equation governing the nutrient concentration $σ$. We establish the existence of local strong solutions , for $ r \geq 1 $ in $d=2$ and $ r \in [1,3] $ in $d=3$. We prove the weak-strong uniqueness holds in both $d = 2, 3$. In addition, for $d = 2$, the uniqueness of weak solutions is obtained for all $η,ν> 0$, and $r \geq 1$, while it holds in $d = 3$ for $r \geq 3$ and $ην\geq 1$ when $r = 3$ under an assumption on $σ$. Moreover, for $d=2$ and $r \in [1,3]$, we obtain that the strong solution exists globally in time. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2605_29779 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Strong Solutions for the Stochastic Cahn-Hilliard Convective Brinkman-Forchheimer Model for Tumor Growth Rawat, Kalpana Sakthivel, Kumarasamy Analysis of PDEs Probability 35R60, 35Q92, 76M35, 35K35, 92C50 In this work, we analyze a diffuse-interface model for tumor growth, subject to multiplicative white noises, posed on a bounded domain $\mathcal{O} \subset \mathbb{R}^d$, $d=2,3$. The model couples a stochastic incompressible convective Brinkman-Forchheimer (CBF) equation or Navier-Stokes equation with damping $η|v|^{r-1}v $ for the averaged velocity field $v$, to a Cahn-Hilliard (CH) equation for the phase field variable $ϕ$ and to a stochastic reaction-diffusion equation governing the nutrient concentration $σ$. We establish the existence of local strong solutions , for $ r \geq 1 $ in $d=2$ and $ r \in [1,3] $ in $d=3$. We prove the weak-strong uniqueness holds in both $d = 2, 3$. In addition, for $d = 2$, the uniqueness of weak solutions is obtained for all $η,ν> 0$, and $r \geq 1$, while it holds in $d = 3$ for $r \geq 3$ and $ην\geq 1$ when $r = 3$ under an assumption on $σ$. Moreover, for $d=2$ and $r \in [1,3]$, we obtain that the strong solution exists globally in time. |
| title | Strong Solutions for the Stochastic Cahn-Hilliard Convective Brinkman-Forchheimer Model for Tumor Growth |
| topic | Analysis of PDEs Probability 35R60, 35Q92, 76M35, 35K35, 92C50 |
| url | https://arxiv.org/abs/2605.29779 |