A one-dimensional inviscid and compressible fluid in a harmonic potential well

Validerad; 2007; 20070925 (strom)
A Hamiltonian model is analyzed for a one-dimensional inviscid compressible fluid. The space-time evolution of the fluid is governed by the following system of the Hamilton-Jacobi and the continuity equations: S-t + 1/2(S-x(2) + omega(2)chi(2)) =0, S(x, 0) = S-0(x); rho(t) + (rho S-x)(x) =0, rho(x, 0) =rho(0)(x).Here S and rho designate the velocity potencial and the mass density, respectively. Unless S-0 is convex, shocks form and the velocity S (x) becomes discontinuous in {0 < omega t < pi/2}. It is demonstrated that there nevertheless exists a unique viscosity-measure solution (S,rho) when S-0 is globally Lipschitz continuous and locally semi-concave while rho(0) is a finite Borel measure. The structure of the velocity and the density is exhibited. For initial data correlated in a certain sense, a class of classical solutions (S,rho) is given. Negative time is also considered, and illustrating examples are given.

Strömberg, ThomasLuleå tekniska universitet,Matematiska vetenskaper(Swepub:ltu)strom (författare)
EPFL, LausanneMatematiska vetenskaper (creator_code:org_t)

Ingår i:Acta Applicandae Mathematicae - An International Survey Journal on Applying Mathematics and Mathematical Applications: Springer Science and Business Media LLC99:2, s. 161-1830167-80191572-9036

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