| Abstract: |
| We establish a solution theory (global weak existence, local strong existence and weak-strong uniqueness) for the incompressible Navier--Stokes--Fourier system with thermal noise, posed on the three-dimensional torus. While in the incompressible deterministic setting the equation for the velocity $u$ can be solved independently of the temperature $\vt$, the inclusion of the effects of thermal fluctuations by means of the GENERIC framework leads to a nonlinear gradient noise term, which couples the dynamics of both variables. Therefore, the analysis of the system for $(u,\vt)$ poses new challenges, which are absent in deterministic Navier--Sokes--Fourier equations. |
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