Dr. Jens Lorenz

• Fall 2024
• Math 305
• Time etc., updated August 12
• Notes, updated Sept. 25

My areas of research are Applied Analysis and Scientific Computing. Specific problems that I have worked on lately include: the stability of shock and spiral waves; the modeling of ocean circulations for climate studies; the transition from smooth to rough attractors and Lyapunov–type numbers. I am broadly interested in partial differential equations and their numerical approximation.

Most of the applications I have worked on are related to fluids, but a recent interest is a nonlinear Black–Scholes equation in financial mathematics. The Black–Scholes equation is used extensively for option pricing; it becomes nonlinear if one assumes dependence of the volatility on the asset price.

• List of Publications
• Publications
• Selected papers
  • Regularity Criteria for Weak Solutions of the Magneto--Micropolar Equations.
  • On Two New Inequalities for Leray Solutions of the Navier--Stokes Equations in $\R^n$.
  • The Magneto-Hydrodynamic Equations: Local Theory and Blow-Up of Solutions
  • On the Large Time Approximation of the Navier--Stokes Equations in $\R^n$ by Stokes Flows
  • Properties at Potential Blow--Up Times for the Incompressible Navier--Stokes Equations
  • On the Blow-Up Criterion of Periodic Solutions for Micropolar Equations in Homogeneous Sobolev Spaces
  • An Example of Self--Acceleration for Incompressible Flows
  • Continuous Spectra and Numerical Eigenvalues
  • A nonlinear Black--Scholes equation
  • Nonlinear Stability of Rotating Patterns
  • Hermite Methods for Hyperbolic IBVPs
  • Stability of viscous profiles: Proofs via dichotomies
  • Numerical approximations of rough invariant curves
  • Stability of viscous shocks on finite intervals
  • A priori estimates in terms of the maximum norm for the solutions of the Navier--Stokes equations
  • Convergence of the solutions of the compressible to the solutions of the incompressible Navier-Stokes equations
  • A note on multistep methods and attracting sets of dynamical systems
  • Stable attracting sets in dynamical systems and in their one step discretizations

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  On the Editorial Board of the Following Publications
  • Boletim da Sociedade Paranaense de Matematica
  • International J. of Business Performance and Supply Chain Modelling
  • International J. of Advanced Operations Management
   

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