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1 [CT044]

[CT044]

[01047] Large Deviations for Two-Dimensional Stochastic Tidal Dynamics Equations driven by Levy Noise

Session Date & Time : 3C (Aug.23, 13:20-15:00)
Type : Contributed Talk
Abstract : The objective is to establish a Wentzell-Freidlin type large deviation principle (LDP) for solution of stochastic tidal dynamics equations driven by Levy Noise. The LDP is equivalent to the Laplace principle in a Polish space. The solution space of the considered equation is Polish. Hence Laplace principle will be established for the stochastic tidal dynamics equations using weak convergence approach for non-negative functionals of a general Poisson random measure and Brownian motion.
Classification : 35Q35, 60H15, 60G65, 60F10
Author(s) :
- HASEENA A (Assistant Professor, Government College Chittur)

[01641] Cut singularity of compressible Stokes flow

Session Date & Time : 3C (Aug.23, 13:20-15:00)
Type : Contributed Talk
Abstract : In this talk we study the cut singularity governed by a compressible Stokes system. The cut is a non-Lipshitz boundary. The divergence of the leading corner singularity vector has different trace values on either sides of cut. In the consequence the pressure solution must have a jump across the streamline emanating from the cut tip. We establish a piecewise regularity of the solution by subtracting the related singular functions.
Classification : 35Q35, 76N10, 76F50
Author(s) :
- Tae Yeob Lee (Pohang University of Science and Technology)
- Jae Ryong Kweon (Pohang University of Science and Technology)

[01840] On the inviscid limit of the stochastic Navier-Stokes equation

Session Date & Time : 3C (Aug.23, 13:20-15:00)
Type : Contributed Talk
Abstract : We study the asymptotic behavior of solutions to the two-dimensional stochasitc Navier-Stokes (SNS) equation in the small viscosity limit. The SNS equation is supplemented with no-slip boundary condition, in which a strong boundary layer shall appear in the limit. Several equivalent dissipation conditions are derived to ensure the convergence hold in the energy space. One novelty of this work is that we do not assume any smallness for the noise.
Classification : 35Q35, 60H15, 76D10
Author(s) :
- Meng Zhao (Shanghai Jiao Tong University)
- Ya-Guang Wang (Shanghai Jiao Tong University)

[02044] On the Analytical Treatment Of the Klein-Gordon Equation

Session Date & Time : 3C (Aug.23, 13:20-15:00)
Type : Contributed Talk
Abstract : Various nonlinear phenomena are modeled by the nonlinear Klein-Gordon equation. Though there are many methods to solve such problems, this work suggests an effective way to solve the Klein-Gordon equation. The technique is a combination of quasilinearization and Picard's method. To illustrate the effectiveness of the method, we consider some numerical examples. This is crucial, as shown in the numerical simulations where our new proposal is efficient, and straightforward to implement.
Classification : 35Q35, 35Q40, 65M99
Author(s) :
- Saurabh Tomar (IIT Kanpur, India)

[02084] A generalized analytical model of the tropical cyclone outer region

Session Date & Time : 3C (Aug.23, 13:20-15:00)
Type : Contributed Talk
Abstract : A generalized analytical model of the outer region of the tropical cyclone is presented. The causes of the variation in the radius of the region outside the eye of tropical cyclones have also been investigated. By simplifying the angular momentum equation and taking into account both the coordinates transformation and the time-dependent radius of maximum winds, the exact solution has been obtained. This model shall provide new insights into tropical cyclone research.
Classification : 35Q35, 35Q30, 76-10
Author(s) :
- Jagdish Prasad Maurya (Rajiv Gandhi University )
- Jagdish Prasad Maurya (Rajiv Gandhi University )

[02103] Global in Time Weak Solutions to Singular 3D Quasi-Geostrophic Systems

Session Date & Time : 3D (Aug.23, 15:30-17:10)
Type : Contributed Talk
Abstract : Geophysicists have studied 3D Quasi-Geostrophic systems extensively. These systems describe stratified flows in the atmosphere on a large time scale and are widely used for forecasting atmospheric circulation. They couple an inviscid transport equation in $\mathbb{R}_{+}\times\Omega$ with an equation on the boundary satisfied by the trace, where $\Omega$ is either $2D$ torus or a bounded convex domain in $\mathbb{R}^2$. In this talk, we show the existence of global in time weak solutions to a family of singular 3D quasi-geostrophic systems with Ekman pumping, where the background density profile degenerates at the boundary. The proof is based on the construction of approximated models which combine the Galerkin method at the boundary and regularization processes in the bulk of the domain. The main difficulty is handling the degeneration of the background density profile at the boundary.
Classification : 35Q35, 76D03
Author(s) :
- Yiran Hu (University of Texas at Austin)

[02475] A New Analytical Approach for Landslide-Generated Waves in U-Bays

Session Date & Time : 3D (Aug.23, 15:30-17:10)
Type : Industrial Contributed Talk
Abstract : We discuss the analytical solution of landslide-generated waves in U-shaped bays. In 2013, Didenkulova and Pelinovsky obtained an explicit analytical solution in the Duhamel integral form. Here we propose a new approach to obtain the analytical solution by applying the Hankel transformation, resulting in a simpler form of solution. Additionally, for the case of Gaussian landslides movement, the analytical solution obtained shows good agreement with the numerical simulation.
Classification : 35Q35, 76B15, 65M12
Author(s) :
- Rani Sulvianuri (Institut Teknologi Bandung (ITB))
- Sri Redjeki Pudjaprasetya (Institut Teknologi Bandung (ITB))

[00460] A Multigrid Method for Many-Electron Schrodinger Equations with ACE

Session Date & Time : 3D (Aug.23, 15:30-17:10)
Type : Contributed Talk
Abstract : We parameterize the many-electron wave functions by atomic cluster expansion $($ACE$)$ approach and calculate ground-state energies and electron densities of some molecule systems within the variational Monte Carlo framework. Compared with the neural-network-based representations, the novelty of our method lies in $($i$)$ a convenient and accurate linear polynomial expansion; $($ii$)$ a hierarchical structure that applies naturally to a multigrid variation; and $($iii$)$ possibly revealing the correlation of the system by increasing the body-order.
Classification : 35Q40, 65N25, 65N35, 81Q05
Author(s) :
- Dexuan Zhou (Beijing Normal University)

[00474] Discrete solitons of discrete Schrodinger equations with general nonlinearities

Session Date & Time : 3D (Aug.23, 15:30-17:10)
Type : Contributed Talk
Abstract : The discrete nonlinear Schrodinger $($DNLS$)$ equations are very important nonlinear lattice models in the nonlinear science, ranging from molecular biology to condensed matter physics. One central problem for the DNLS equations is the existence of discrete solitons. We will report some recent progress on the existence and multiplicity of discrete solitons for a class of DNLS equations with general nonlinearities.
Classification : 35Q51, 35Q55, 39A12, 39A70
Author(s) :
- Genghong Lin (Guangzhou University)

[02490] Mathematical Model of COVID-19 Dynamics under Vaccination Strategy and Immunity Waning using the Nigerian Demography

Session Date & Time : 3D (Aug.23, 15:30-17:10)
Type : Contributed Talk
Abstract : An endemic mathematical model with five compartments on the transmission dynamics of COVID-19 is formulated and analysed using Nigerian demography. The compartments are, susceptible, vaccinated, exposed, infected and recovered. The model is studied qualitatively using the stability theory of differential equations and the basic reproductive number is obtained using the next generational matrix approach. We obtain the global stability conditions for disease-free and endemic equilibria. The model assessed the scenario whereby the waning immunity for the disease occurs in order to check the epidemic peaks. The numerical simulation results show that the disease would continue to be endemic in the population as long as the immunity waning rates increase. Overall, our findings imply that the epidemic peak can be reduced by increasing vaccination and vaccine efficacy rates.
Classification : 35Q51, 26A18, 37B25
Author(s) :
- Olumuyiwa James Peter (University of Medical Sciences)
- Rabiu Musa (Technion - Israel Institute of Technology)