4 papers
Joint inviscid, incompressible, and continuous phenotype limit in nonlocal models of tissue growth
Chen-Chih Lai, Hongbo Lu
We rigorously derive the joint limit of vanishing viscosity, singular pressure, and discrete-to-continuous phenotype structure in a class of tissue growth models. Starting from a v…
Moment Estimates and DeepRitz Methods on Learning Diffusion Systems with Non-gradient Drifts
Fanze Kong, Chen-Chih Lai, Yubin Lu
Conservative-dissipative dynamics are ubiquitous across a variety of complex open systems. We propose a data-driven two-phase method, the Moment-DeepRitz Method, for learning drift…
Moment Estimate and Variational Approach for Learning Generalized Diffusion with Non-gradient Structures
Fanze Kong, Chen-Chih Lai, Yubin Lu
This paper proposes a data-driven learning framework for identifying governing laws of generalized diffusions with non-gradient components. By combining energy dissipation laws wit…
Weak and mild solutions to the MHD equations and the viscoelastic Navier-Stokes equations with damping in Wiener amalgam spaces
Chen-Chih Lai
We study the three-dimensional incompressible magnetohydrodynamic (MHD) equations and the incompressible viscoelastic Navier-Stokes equations with damping. Building on techniques d…