Low Mach number limit for the global large solutions to the 2D Navier–Stokes–Korteweg system in the critical $$\widehat{L^p}$$ framework
Copyright policy )Low Mach number limit for the global large solutions to the 2D Navier–Stokes–Korteweg system in the critical $$\widehat{L^p}$$ framework
In the present paper, we consider the compressible Navier--Stokes--Korteweg system on the $2$D whole plane and show that a unique global solution exists in the scaling critical Fourier--Besov spaces for arbitrary large initial data provided that the Mach number is sufficiently small. Moreover, we also show that the global solution converges to the $2$D incompressible Navier--Stokes flow in the singular limit of zero Mach number. The key ingredient of the proof lies in the nonlinear stability estimates around the large incompressible flow via the Strichartz estimate for the linearized equations in Fourier--Besov spaces.
- Anhui University China (People's Republic of)
- Nagoya City University Japan
Compressible Navier-Stokes equations, Smoothness and regularity of solutions to PDEs, Initial value problems for systems of nonlinear higher-order PDEs, Navier-Stokes equations for incompressible viscous fluids, Existence problems for PDEs: global existence, local existence, non-existence, Uniqueness problems for PDEs: global uniqueness, local uniqueness, non-uniqueness, incompressible Navier-Stokes flow, Critical exponents in context of PDEs, Mathematics - Analysis of PDEs, KdV equations (Korteweg-de Vries equations), FOS: Mathematics, Navier-Stokes equations, compressible Navier-Stokes-Korteweg system, Singular perturbations in context of PDEs, Analysis of PDEs (math.AP)
Compressible Navier-Stokes equations, Smoothness and regularity of solutions to PDEs, Initial value problems for systems of nonlinear higher-order PDEs, Navier-Stokes equations for incompressible viscous fluids, Existence problems for PDEs: global existence, local existence, non-existence, Uniqueness problems for PDEs: global uniqueness, local uniqueness, non-uniqueness, incompressible Navier-Stokes flow, Critical exponents in context of PDEs, Mathematics - Analysis of PDEs, KdV equations (Korteweg-de Vries equations), FOS: Mathematics, Navier-Stokes equations, compressible Navier-Stokes-Korteweg system, Singular perturbations in context of PDEs, Analysis of PDEs (math.AP)
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