48 research outputs found
Energy distribution of the solutions of elastic wave propagation problems in stratified media R3
This paper deals with the asymptotic energy distributions for large times of the solutions of elastic wave propagation problems in stratified media R3. We construct asymptotic wage functions which approximate the solutions for large times and claculate the asymptotic energy of the solutions using these asymptotic wave functions. In particular, it is shown that the energy of Stoneley wave is asymptotically concentrated along the interface
On a Navier–Stokes–Ohm problem from plasma physics in multi connected domains
We consider a model from electro-magneto-hydrodynamics describing a plasma in bounded multi connected domains. A nontrivial solution exists for magnetic fields as the equilibrium of this model. Nonlinear stability of the nontrivial solution is proved based on time weighted maximal Lp-regularity
Free boundary problems for a viscous incompressible fluid(Kyoto Conference on the Navier-Stokes Equations and their Applications)
Maximal regularity for the Cauchy problem of the heat equation in BMO
We consider maximal regularity for the Cauchy problem of the heat equation in a class of bounded mean oscillations (B M O). Maximal regularity for non-reflexive Banach spaces is not obtained by the established abstract theory. Based on the symmetric characterization of B M O-expression, we obtain maximal regularity for the heat equation in B M O and its sharp trace estimate. Our result shows that the homogeneous initial estimate obtained by Stein [50] and Koch–Tataru [32] can be strengthened up to the inhomogeneous estimate for the external forces and the obtained estimates can be applicable to quasilinear problems. Our method is based on integration by parts and can also be applicable to other type of parabolic problems
Global existence of solutions to 2-D Navier-Stokes flow with non-decaying initial data in half-plane
We investigate the Navier-Stokes initial boundary value problem in the
half-plane with initial data
or with non decaying initial data . We introduce a technique that allows to solve the two-dimesional
problem, further, but not least, it can be also employed to obtain weak
solutions, as regards the non decaying initial data, to the three-dimensional
Navier-Stokes IBVP. This last result is the first of its kind