On the existence of global solutions of a system of semilinear parabolic equations with nonlinear nonlocal boundary conditions

We consider a general compressible viscous and heat conducting fluid confined between two parallel plates and heated from the bottom. The time evolution of the fluid is described by the Navier–Stokes–Fourier system considered in the regime of low Mach and Froude numbers suitably interrelated. Surprisingly and differently to the case of Neumann boundary conditions for the temperature, the asymptotic limit is identified as the Oberbeck–Boussinesq system supplemented with non-local boundary conditions for the temperature deviation.

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Rigorous Derivation of the Oberbeck–Boussinesq Approximation Revealing Unexpected Term

Bella

Feireisl

Oschmann

2023

Commun. Math. Phys.

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Initial boundary value problem for a semilinear parabolic equation with absorption and nonlinear nonlocal boundary condition*

Gladkov

2017

Lith Math J

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On the absence of global solutions of a system of ordinary differential equations

Kon'kov¹

2022

Sb. Math.

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On the existence of global solutions of a system of semilinear parabolic equations with nonlinear nonlocal boundary conditions

Cited by 8 publications

References 15 publications

Rigorous Derivation of the Oberbeck–Boussinesq Approximation Revealing Unexpected Term

Rigorous Derivation of the Oberbeck–Boussinesq Approximation Revealing Unexpected Term

Initial boundary value problem for a semilinear parabolic equation with absorption and nonlinear nonlocal boundary condition*

On the absence of global solutions of a system of ordinary differential equations

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