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

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 $R^2_+$ with initial data $u_0 \in L^\infty(R^2_+)\cap J_0^2(R^2_+)$ or with non decaying initial data $u_0\in L^\infty(R^2_+) \cap J_0^p(R^2_+), p > 2$ . 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