On the existence of solutions for a nonlinear stochastic partial differential equation arising as a model of phytoplankton aggregation

TL;DR

This paper investigates the existence of solutions for a complex nonlinear stochastic PDE modeling phytoplankton aggregation, incorporating diffusion, chemotaxis, and noise, using advanced mathematical techniques.

Contribution

It establishes the existence of mild solutions for a novel SPDE model of phytoplankton aggregation, combining chemotaxis and stochastic noise.

Findings

Existence of mild solutions proven

Utilizes weak and tightness arguments

Addresses a biologically motivated nonlinear SPDE

Abstract

In this paper, we are interested in the analytical study of a nonlinear Stochastic Partial Differential Equation (SPDE) arising as a model of phytoplankton aggregation. This SPDE consists in a diffusion equation with a chemotaxis term responsible of self-attraction of phytoplankton cells and a multiplicative branching noise. Existence of mild solutions is established through weak and tightness arguments.