Global large solutions to the two-dimensional compressible Navier–Stokes equations

We obtain the global large solutions to the compressible Navier-Stokes equations in $\mathbb{R}^2$. The solution is large in the sense that there is no smallness assumption applied to one component of the initial incompressible velocity.

[1]  Takaaki Nishida,et al.  The Initial Value Problem for the Equations of Motion of compressible Viscous and Heat-conductive Fluids. , 1979 .

[2]  Emil Wiedemann,et al.  Dissipative measure-valued solutions to the compressible Navier–Stokes system , 2015, Calculus of Variations and Partial Differential Equations.

[3]  R. Danchin,et al.  Fourier Analysis and Nonlinear Partial Differential Equations , 2011 .

[4]  Zhouping Xin,et al.  Global well‐posedness of classical solutions with large oscillations and vacuum to the three‐dimensional isentropic compressible Navier‐Stokes equations , 2010, 1004.4749.

[5]  Jiang Xu,et al.  Optimal Time-decay Estimates for the Compressible Navier–Stokes Equations in the Critical Lp Framework , 2016, 1605.00893.

[6]  Raphaël Danchin,et al.  A Global Existence Result for the Compressible Navier–Stokes Equations in the Critical Lp Framework , 2010 .

[7]  Raphaël Danchin,et al.  Global existence in critical spaces for compressible Navier-Stokes equations , 2000 .

[8]  Matthias Kotschote,et al.  Dynamical Stability of Non-Constant Equilibria for the Compressible Navier–Stokes Equations in Eulerian Coordinates , 2014 .

[9]  David Hoff,et al.  Compressible Flow in a Half-Space with Navier Boundary Conditions , 2005 .

[10]  Takaaki Nishida,et al.  Initial boundary value problems for the equations of motion of compressible viscous and heat-conductive fluids , 1983 .

[11]  Zhouping Xin,et al.  Blowup of smooth solutions to the compressible Navier‐Stokes equation with compact density , 1998 .

[12]  Ting Zhang,et al.  Global Solutions to the Isentropic Compressible Navier-Stokes Equations with a Class of Large Initial Data , 2016, SIAM J. Math. Anal..

[13]  J. Nash,et al.  Le problème de Cauchy pour les équations différentielles d'un fluide général , 1962 .

[14]  Boris Haspot,et al.  Existence of Global Strong Solutions in Critical Spaces for Barotropic Viscous Fluids , 2010, 1005.0706.

[15]  Piotr B. Mucha,et al.  Compressible Navier-Stokes system : large solutions and incompressible limit , 2016, 1603.07213.

[16]  Xiaoping Zhai,et al.  Global Large Solutions and Incompressible Limit for the Compressible Navier–Stokes Equations , 2018, Journal of Mathematical Fluid Mechanics.

[17]  Wei Wang,et al.  Global Well-Posedness of Compressible Navier–Stokes Equations for Some Classes of Large Initial Data , 2011, 1111.2203.

[18]  Qionglei Chen,et al.  Global well‐posedness for compressible Navier‐Stokes equations with highly oscillating initial velocity , 2009, 0907.4540.

[19]  Raphael Danchin,et al.  A Lagrangian approach for the compressible Navier-Stokes equations , 2012, 1201.6203.

[20]  Ping Zhang,et al.  Global solutions to the 3-D incompressible inhomogeneous Navier–Stokes system , 2012 .

[21]  E. Feireisl,et al.  Suitable weak solutions to the Navier-Stokes equations of compressible viscous fluids , 2011 .

[22]  Eduard Feireisl,et al.  Dynamics of Viscous Compressible Fluids , 2004 .

[23]  E. Feireisl,et al.  On the Existence of Globally Defined Weak Solutions to the Navier—Stokes Equations , 2001 .

[24]  P. Lions Mathematical topics in fluid mechanics , 1996 .

[25]  David Hoff,et al.  Global Solutions of the Navier-Stokes Equations for Multidimensional Compressible Flow with Discontinuous Initial Data , 1995 .

[26]  Ping Zhang,et al.  Global Well-posedness of Incompressible Inhomogeneous Fluid Systems with Bounded Density or Non-Lipschitz Velocity , 2013 .

[27]  Lingbing He,et al.  Global Stability of Large Solutions to the 3D Compressible Navier–Stokes Equations , 2017, Archive for Rational Mechanics and Analysis.