In a recent work on the quantization of a massless scalar field in a particular colliding plane wave space-time, we computed the vacuum expectation value of the stress-energy tensor on the physical state which corresponds to the Minkowski vacuum before the collision of the waves. We did such a calculation in a region close to both the Killing-Cauchy horizon and the folding singularities that su...

one of the most remarkable basis of the gravity data inversion is the recognition of sharp boundaries between an ore body and its host rocks during the interpretation step. therefore, in this work, it is attempted to develop an inversion approach to determine a 3d density distribution that produces a given gravity anomaly. the subsurface model consists of a 3d rectangular prisms of known sizes ...

We show that a smooth, small enough Cauchy datum launches a unique classical solution of the relativistic Vlasov-Darwin (RVD) system globally in time. A similar result is claimed in [15] following the work in [13]. Our proof does not require estimates derived from the conservation of the total energy, nor those previously given on the transverse component of the electric field. These estimates ...

We characterize boundedness and compactness of weighted composition operators from the space of Cauchy integral transforms to logarithmic weighted-type spaces. We also manage to compute norm of weighted composition operators acting between these spaces.

We consider the Cauchy problem for the nonlinear Schrödinger equations with energy-critical damping. We prove the existence of global intime solutions for general initial data in the energy space. Our results extend some results from [1, 2].

The Cauchy problem for 1-dimensional nonlinear stochastic partial differential equations is studied. The uniqueness and existence of solutions in Hp(T )-space are proved. 1991 Mathematics Subject Classification. 60H15, 35R60.

In this paper, we establish the global well-posedness of the Cauchy problem for the Gross-Pitaevskii equation with an angular momentum rotational term in which the angular velocity is equal to the isotropic trapping frequency in the space R .

We apply the I-method to prove that the Cauchy problem of a higher-order Schrödinger equation is globally well-posed in the Sobolev space Hs(R) with s > 6/7.

This note shows the existence of a sharp bilinear estimate for the Bourgain-type space and gives its application to the optimal local well/illposedness of the Cauchy problem for the Benjamin equation.

This work discusses the apriori possible asymptotic behavior to the future, for (vacuum) space-times which are geodesically complete to the future, and which admit a foliation by constant mean curvature compact Cauchy surfaces.