Sharp decay estimates for Oldroyd-B model with only fractional stress tensor diffusion

2021 ◽  
pp. 109332
Author(s):  
Peixin Wang ◽  
Jiahong Wu ◽  
Xiaojing Xu ◽  
Yueyuan Zhong
Author(s):  
Philip Isett

This chapter deals with the gluing of solutions and the relevant theorem (Theorem 12.1), which states the condition for a Hölder continuous solution to exist. By taking a Galilean transformation if necessary, the solution can be assumed to have zero total momentum. The cut off velocity and pressure form a smooth solution to the Euler-Reynolds equations with compact support when coupled to a smooth stress tensor. The proof of Theorem (12.1) proceeds by iterating Lemma (10.1) just as in the proof of Theorem (10.1). Applying another Galilean transformation to return to the original frame of reference, the theorem is obtained.


2011 ◽  
Vol 56 (2) ◽  
pp. 503-508 ◽  
Author(s):  
R. Pęcherski ◽  
P. Szeptyński ◽  
M. Nowak

An Extension of Burzyński Hypothesis of Material Effort Accounting for the Third Invariant of Stress Tensor The aim of the paper is to propose an extension of the Burzyński hypothesis of material effort to account for the influence of the third invariant of stress tensor deviator. In the proposed formulation the contribution of the density of elastic energy of distortion in material effort is controlled by Lode angle. The resulted yield condition is analyzed and possible applications and comparison with the results known in the literature are discussed.


2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Hui Wang ◽  
Caisheng Chen

AbstractIn this paper, we are interested in $L^{\infty }$ L ∞ decay estimates of weak solutions for the doubly nonlinear parabolic equation and the degenerate evolution m-Laplacian equation not in the divergence form. By a modified Moser’s technique we obtain $L^{\infty }$ L ∞ decay estimates of weak solutiona.


2021 ◽  
Vol 2021 (3) ◽  
Author(s):  
J.M. Drummond ◽  
H. Paul

Abstract We consider α′ corrections to the one-loop four-point correlator of the stress- tensor multiplets in $$ \mathcal{N} $$ N = 4 super Yang-Mills at order 1/N4. Holographically, this is dual to string corrections of the one-loop supergravity amplitude on AdS5 × S5. While this correlator has been considered in Mellin space before, we derive the corresponding position space results, gaining new insights into the analytic structure of AdS loop amplitudes. Most notably, the presence of a transcendental weight three function involving new singularities is required, which has not appeared in the context of AdS amplitudes before. We thereby confirm the structure of string corrected one-loop Mellin amplitudes, and also provide new explicit results at orders in α′ not considered before.


2020 ◽  
Vol 72 (1) ◽  
Author(s):  
Kazutoshi Imanishi ◽  
Makiko Ohtani ◽  
Takahiko Uchide

Abstract A driving stress of the Mw5.8 reverse-faulting Awaji Island earthquake (2013), southwest Japan, was investigated using focal mechanism solutions of earthquakes before and after the mainshock. The seismic records from regional high-sensitivity seismic stations were used. Further, the stress tensor inversion method was applied to infer the stress fields in the source region. The results of the stress tensor inversion and the slip tendency analysis revealed that the stress field within the source region deviates from the surrounding area, in which the stress field locally contains a reverse-faulting component with ENE–WSW compression. This local fluctuation in the stress field is key to producing reverse-faulting earthquakes. The existing knowledge on regional-scale stress (tens to hundreds of km) cannot predict the occurrence of the Awaji Island earthquake, emphasizing the importance of estimating local-scale (< tens of km) stress information. It is possible that the local-scale stress heterogeneity has been formed by local tectonic movement, i.e., the formation of flexures in combination with recurring deep aseismic slips. The coseismic Coulomb stress change, induced by the disastrous 1995 Mw6.9 Kobe earthquake, increased along the fault plane of the Awaji Island earthquake; however, the postseismic stress change was negative. We concluded that the gradual stress build-up, due to the interseismic plate locking along the Nankai trough, overcame the postseismic stress reduction in a few years, pushing the Awaji Island earthquake fault over its failure threshold in 2013. The observation that the earthquake occurred in response to the interseismic plate locking has an important implication in terms of seismotectonics in southwest Japan, facilitating further research on the causal relationship between the inland earthquake activity and the Nankai trough earthquake. Furthermore, this study highlighted that the dataset before the mainshock may not have sufficient information to reflect the stress field in the source region due to the lack of earthquakes in that region. This is because the earthquake fault is generally locked prior to the mainshock. Further research is needed for estimating the stress field in the vicinity of an earthquake fault via seismicity before the mainshock alone.


Sign in / Sign up

Export Citation Format

Share Document