arXiv subjects

S. Zamorano

Publications and source records attributed to S. Zamorano.

3 recordsLinked to original sources

arXiv2020

The stability for an inverse problem of bottom recovering in water-waves

In this article we deal with a class of geometric inverse problem for bottom detection by one single measurement on the free surface in water--waves. We found upper and lower bounds for the size of the region enclosed between two different bottoms, in terms of Neumann and/or Dirichlet data on the free surface. Starting from the general water--waves system in bounded domains with side walls, we manage to formulate the problem in terms of the Dirichlet to Neumann operator and thus, as an elliptic problem in a bounded domain with Neumann homogeneous condition on the rigid boundary. Then we study the properties of the Dirichlet to Neumann map and analyze the called method of size estimation.

math.AP↗

arXiv2016

The Turnpike Property for Two-Dimensional Navier-Stokes Equations

This paper is devoted to the study of the turnpike phenomenon arising in the optimal distributed control tracking-type problem for the Navier-Stokes equations. We obtain a positive answer to this property in the case when the controls are time-dependent functions, and also when are independent of time. In both cases we prove an exponential turnpike property assuming that the stationary optimal state satisfy certain properties of smallness.

math.OC↗

arXiv2016

Size estimates of an obstacle in a stationary Stokes fluid

In this work we are interested in estimating the size of a cavity D immersed in a bounded domain Ω, contained in R^d, d=2,3, filled with a viscous fluid governed by the Stokes system, by means of velocity and Cauchy forces on the external boundary of Ω. More precisely, we establish some lower and upper bounds in terms of the difference between the external measurements when the obstacle is present and without the object. The proof of the result is based on interior regularity results and quantitative estimates of unique continuation for the solution of the Stokes system.

math.AP↗