Analytical solutions to the pressureless Euler-Korteweg equations with free boundary

KdV equations (Korteweg-de Vries equations) (35Q53) Analyticity in context of PDEs (35A20) Free boundary problems for PDEs (35R35) Symmetries, invariants, etc. in context of PDEs (35B06) Self-similar solutions to PDEs (35C06) Euler equations (35Q31)

Cites Work

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Translation of J. D. van der Waals' ``The thermodynamic theory of capillarity under the hypothesis of a continuous variation of density
Explicitly self-similar solutions for the Euler/Navier-Stokes-Korteweg equations in \(R^N\)
Global well-posedness of the Euler-Korteweg system for small irrotational data
Some exact blowup solutions to the pressureless Euler equations in \(\mathbb R^{N}\)
Exact, rotational, infinite energy, blowup solutions to the 3-dimensional Euler equations
Some special solutions of the multidimensional Euler equations in \(\mathbb R^N\)
Blow-up phenomena of solutions to the Euler equations for compressible fluid flow
Kreiss symmetrizer and boundary conditions for the Euler-Korteweg system in a half space
Convergence to nonlinear diffusion waves for solutions of Euler-Korteweg equations with damping
Perturbational blowup solutions to the compressible 1-dimensional Euler equations
Free boundary value problem for damped Euler equations and related models with vacuum
Analytical blowup solutions to the compressible Euler equations with time-depending damping
Vortical and self-similar flows of 2D compressible Euler equations
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Nonstationary flows of viscous and ideal fluids in \(R^3\)
Asymptotic behavior of solutions to the Euler-Korteweg equations with time-dependent damping
Dispersive Smoothing for the Euler--Korteweg Model
Madelung, Gross–Pitaevskii and Korteweg
Analytical solutions to the Navier–Stokes equations
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Stability properties of the Euler–Korteweg system with nonmonotone pressures
Small energy traveling waves for the Euler–Korteweg system
On the well-posedness for the Euler-Korteweg model in several space dimensions
Analytical solutions to the compressible Euler equations with time-dependent damping and free boundaries

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