Analysis of Partial Differential Equations (APDE)
http://hdl.handle.net/20.500.11824/1
Tue, 04 Oct 2022 14:26:47 GMT2022-10-04T14:26:47ZMotion of a rigid body in a compressible fluid with Navier-slip boundary condition
http://hdl.handle.net/20.500.11824/1518
Motion of a rigid body in a compressible fluid with Navier-slip boundary condition
Necasova, S.; Ramaswamy, M.; Roy, A.; Schlömerkemper, A.
In this work, we study the motion of a rigid body in a bounded domain which is filled with a compressible isentropic fluid. We consider the Navier-slip boundary condition at the interface as well as at the boundary of the domain. This is the first mathematical analysis of a compressible fluid-rigid body system where Navier-slip boundary conditions are considered. We prove existence of a weak solution of the fluid-structure system up to collision.
Fri, 25 Nov 2022 00:00:00 GMThttp://hdl.handle.net/20.500.11824/15182022-11-25T00:00:00ZSharp local smoothing estimates for Fourier integral operators
http://hdl.handle.net/20.500.11824/1513
Sharp local smoothing estimates for Fourier integral operators
Beltran D.; Hickman J.; Sogge C.D.
The theory of Fourier integral operators is surveyed, with an emphasis on local smoothing estimates and their applications. After reviewing the classical background, we describe some recent work of the authors which established sharp local smoothing estimates for a natural class of Fourier integral operators. We also show how local smoothing estimates imply oscillatory
integral estimates and obtain a maximal variant of an oscillatory integral estimate of Stein. Together with an oscillatory integral counterexample of Bourgain, this shows that our local smoothing estimates are sharp in odd spatial dimensions. Motivated by related counterexamples, we formulate local smoothing conjectures which take into account natural geometric assumptions
arising from the structure of the Fourier integrals.
Tue, 01 Jan 2019 00:00:00 GMThttp://hdl.handle.net/20.500.11824/15132019-01-01T00:00:00ZA∞ condition for general bases revisited: complete classification of definitions
http://hdl.handle.net/20.500.11824/1504
A∞ condition for general bases revisited: complete classification of definitions
Kosz, D.
We refer to the discussion on different characterizations of the
A∞ class of weights, initiated by Duoandikoetxea, Martín-Reyes, and Ombrosi
[Math. Z. 282 (2016), pp. 955–972]. Twelve definitions of the A∞ condition are
considered. For cubes in Rd every two conditions are known to be equivalent,
while for general bases we have a trichotomy: equivalence, one-way implication,
or no dependency may occur. In most cases the relations between different
conditions have already been established. Here all the unsolved cases are
treated and, as a result, a full diagram of the said relations is presented.
Fri, 27 May 2022 00:00:00 GMThttp://hdl.handle.net/20.500.11824/15042022-05-27T00:00:00ZCorrigendum to: An extension problem and trace Hardy inequality for the sublaplacian on H-type groups
http://hdl.handle.net/20.500.11824/1503
Corrigendum to: An extension problem and trace Hardy inequality for the sublaplacian on H-type groups
Roncal, L.; Thangavelu, S.
Recently we have found a couple of errors in our paper entitled An extension problem
and trace Hardy inequality for the sub-Laplacian on $H$-type groups, Int. Math. Res.
Not. IMRN (2020), no. 14, 4238--4294. They concern Propositions 3.12--3.13, and Theorem
1.5, Corollary 1.6 and Remark 4.10. The purpose of this corrigendum is to point out the
errors and supply necessary modifications where it is applicable.
Wed, 10 Mar 2021 00:00:00 GMThttp://hdl.handle.net/20.500.11824/15032021-03-10T00:00:00Z