Classical solution for compressible Navier-Stokes-Korteweg equations with zero sound speed
Year: 2025
Type: article
Abstract: We consider the compressible Navier-Stokes-Korteweg equations describing the dynamics of a liquid-vapor mixture with diffuse interphase in R d {{\mathbb{R}}}^{d} with d ≥ 3 d\ge 3 when the initial perturbation is suitably small. In particular, when the base sound speed P ′ ( ρ ¯ ) = 0 \sqrt{P^{\prime} \left(\bar{\rho })}=0 , we first give the global existence and optimal L 2 {L}^{2} -decay rate of the smooth solution, where the optimality means that the decay rate of the solution is the same as that for the corresponding linearized system, and there is no decay loss for the highest-order spatial derivatives of the solution. Then, we establish space-time behavior of the solution based on Green’s function method. It is obviously different from the case P ′ ( ρ ¯ ) > 0 \sqrt{P^{\prime} \left(\bar{\rho })}\gt 0 , which obeys the generalized Huygens’ principle as the compressible Navier-Stokes equations.
Source: Advances in Nonlinear Analysis
Authors: Mengqian Liu, Zhigang Wu
Institutions: Donghua University, Hubei University of Automotive Technology
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: gold
Estimated APC paid: $1,469
OpenAlex ID: W4409506617