Analysis of Partial Differential Equations (APDE)
http://hdl.handle.net/20.500.11824/1
2022-08-18T19:36:29ZA∞ 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.
2022-05-27T00:00:00ZCorrigendum 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.
2021-03-10T00:00:00ZENERGY CONSERVATION FOR 2D EULER WITH VORTICITY IN L(log L)α*
http://hdl.handle.net/20.500.11824/1486
ENERGY CONSERVATION FOR 2D EULER WITH VORTICITY IN L(log L)α*
Ciampa, G.
In these notes we discuss the conservation of the energy for weak solutions of the twodimensional incompressible Euler equations. Weak solutions with vorticity in (Formula presented) with p > 3/2 are always conservative, while for less integrable vorticity the conservation of the energy may depend on the approximation method used to construct the solution. Here we prove that the canonical approximations introduced by DiPerna and Majda provide conservative solutions when the initial vorticity is in the class L(logL)α with α > 1/2.
2022-01-01T00:00:00ZExistence of a weak solution to a nonlinear fluid-structure interaction problem with heat exchange
http://hdl.handle.net/20.500.11824/1485
Existence of a weak solution to a nonlinear fluid-structure interaction problem with heat exchange
Mácha, V.; Muha, B.; Nečasová, S.; Roy, A.; Trifunović, S.
In this paper, we study a nonlinear interaction problem between a thermoelastic shell and a heat-conducting fluid. The shell is governed by linear thermoelasticity equations and encompasses a time-dependent domain which is filled with a fluid governed by the full Navier-Stokes-Fourier system. The fluid and the shell are fully coupled, giving rise to a novel nonlinear moving boundary fluid-structure interaction problem involving heat exchange. The existence of a weak solution is obtained by combining three approximation techniques–decoupling, penalization and domain extension. In particular, the penalization and the domain extension allow us to use the methods already developed for compressible fluids on moving domains. In such a way, the proof is more elegant and the analysis is drastically simplified. Let us stress that this is the first time the heat exchange in the context of fluid-structure interaction problems is considered.
2022-01-01T00:00:00Z