Explicitly self-similar solutions for the Euler/Navier-Stokes-Korteweg equations in RN

[1]  T. Simula Vortices , 2019, Quantised Vortices.

[2]  Yan Xu,et al.  A local discontinuous Galerkin method for the (non)-isothermal Navier-Stokes-Korteweg equations , 2015, J. Comput. Phys..

[3]  E. Fan,et al.  The Cartesian Vector Solutions for the N‐Dimensional Compressible Euler Equations , 2015 .

[4]  Pascal Noble,et al.  Stability Theory for Difference Approximations of Euler-Korteweg Equations and Application to Thin Film Flows , 2013, SIAM J. Numer. Anal..

[5]  Huijiang Zhao,et al.  Existence and nonlinear stability of stationary solutions to the full compressible Navier–Stokes–Korteweg system , 2014 .

[6]  Charalambos Makridakis,et al.  Energy consistent discontinuous Galerkin methods for the Navier-Stokes-Korteweg system , 2012, Math. Comput..

[7]  Hongli An,et al.  Supplement to "Self-similar solutions with elliptic symmetry for the compressible Euler and Navier-Stokes equations in RN" [Commun. Nonlinear Sci. Numer. Simul. 17 (2012) 4524-4528] , 2013, Commun. Nonlinear Sci. Numer. Simul..

[8]  I. F. Barna,et al.  Analytic solutions for the one-dimensional compressible Euler equation with heat conduction closed with different kind of equation of states , 2012, 1209.0607.

[9]  Corentin Audiard,et al.  Dispersive Smoothing for the Euler-Korteweg Model , 2012, SIAM J. Math. Anal..

[10]  Zhenhua Guo,et al.  Analytical solutions to the compressible Navier–Stokes equations with density-dependent viscosity coefficients and free boundaries , 2012 .

[11]  Jean-Claude Saut,et al.  Madelung, Gross–Pitaevskii and Korteweg , 2011, 1111.4670.

[12]  Manwai Yuen,et al.  Self-Similar Solutions with Elliptic Symmetry for the Compressible Euler and Navier-Stokes Equations in R N , 2011, 1104.3687.

[13]  J. Höwing Stability of large- and small-amplitude solitary waves in the generalized Korteweg–de Vries and Euler–Korteweg/Boussinesq equations , 2011 .

[14]  I. F. Barna,et al.  Self-Similar Solutions of Three-Dimensional Navier—Stokes Equation , 2011, 1102.5504.

[15]  C. Audiard Kreiss symmetrizer and boundary conditions for the Euler–Korteweg system in a half space , 2010 .

[16]  S. Lou,et al.  Vortices, circumfluence, symmetry groups, and Darboux transformations of the (2+1) -dimensional Euler equation. , 2007, Physical review. E, Statistical, nonlinear, and soft matter physics.

[17]  Christian Rohde,et al.  On local and non‐local Navier‐Stokes‐Korteweg systems for liquid‐vapour phase transitions , 2005 .

[18]  D. Hoff,et al.  Symmetric Nonbarotropic Flows with Large Data and Forces , 2004 .

[19]  Hi Jun Choe,et al.  Strong solutions of the Navier-Stokes equations for isentropic compressible fluids , 2003 .

[20]  Jiequan Li Global Solution of an Initial-Value Problem for Two-Dimensional Compressible Euler Equations , 2002 .

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

[22]  Changjiang Zhu,et al.  COMPRESSIBLE NAVIER-STOKES EQUATIONS WITH DENSITY-DEPENDENT VISCOSITY AND VACUUM , 2001 .

[23]  Y. Charles Li,et al.  Lax Pairs and Darboux Transformations for Euler Equations , 2001, math/0101214.

[24]  Song Jiang,et al.  On Spherically Symmetric Solutions¶of the Compressible Isentropic Navier–Stokes Equations , 2001 .

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

[26]  Andrew P. Bassom,et al.  Similarity Reductions and Exact Solutions for the Two‐Dimensional Incompressible Navier–Stokes Equations , 1999 .

[27]  Tong Zhang,et al.  Axisymmetric Solutions of the Euler Equations for Polytropic Gases , 1998 .

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

[29]  Tong Zhang,et al.  Exact spiral solutions of the two-dimensional Euler equations , 1996 .

[30]  Gui-Qiang G. Chen,et al.  Global solutions to the compressible Euler equations with geometrical structure , 1996 .