Walter Rusin

Department of Mathematics
Oklahoma State University

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Research

My research interest lie in the area of the analysis of partial differential equations arising in fluid dynamics.

My research is funded through the NSF Grant DMS-1311964.

Brief description

My Research Statement in pdf form (updated October 2015)

List of publications

	W. Rusin, Artificial compressibility in the context of Euler equations. Submitted.
	W. Rusin, Persistence and loss of regularity for the non-dissipative viscous magneto-geostrophic equation. Submitted.
	I. Kukavica, W. Rusin, and M. Ziane, An anisotropic partial regularity criterion for the Navier-Stokes equations. Submitted.
	S. Friedlander, W. Rusin, On the smoothing effect in the kinematic dynamo equations in critical spaces. Journal of Mathematical Fluid Mechanics, Volume 17 (2015), Issue 1, pp.145-153
	I. Kukavica, W. Rusin, and M. Ziane, A class of large $BMO^{-1}$ non-oscillatory data for the Navier-Stokes equations. Journal of Mathematical Fluid Mechanics, 16 (2014), 293-305.
	I. Kukavica, Y. Pei, W. Rusin, and M. Ziane, Primitive Equations With Continuous Initial Data. Nonlinearity 27 (2014), 1135-1155.
	S. Friedlander, W. Rusin, and V. Vicol, The magneto-geostrophic equations: a survey. Proceedings of the St. Petersburg Mathematical Society, Volume XV: Advances in Mathematical Analysis of Partial Differential Equations, American Mathematical Society, 2014.
	S. Benachour, I. Kukavica, W. Rusin, and M. Ziane, Anisotropic estimates for the two-dimensional Kuramoto-Sivashinsky equation. Journal of Dynamics and Differential Equations, 26 (1014), 461-476.
	S. Friedlander and W. Rusin, On the second iterate for critically diffusive active scalar equations. Journal of Mathematical Fluid Mechanics, 15 (2013), no. 3, 481-492.
	I. Kukavica, W. Rusin, and M. Ziane, A class of solutions to the Navier-Stokes equations with large data. Journal of Differential Equations, 255 (2013), no. 7, 1492-1514.
	I. Kukavica, W. Rusin, and M. Ziane, {Solutions to Navier-Stokes equations for large oscillatory data. Advances in Differential Equations, 18 (2013), no. 5/6, 549-586.
	S. Friedlander, W. Rusin, and V. Vicol, On the supercritically diffusive magneto-geostrophic equations. Nonlinearity, 25 (2012), no. 11, 3071-3097.
	W. Rusin, Inviscid limits for active scalar equations with mildly singular gradients. Journal of Mathematical Fluid Mechanics 15 (2013), no. 2, 415-423.
	W. Rusin, Incompressible Navier-Stokes equations as a limit of a nonlinear parabolic system. Journal of Mathematical Fluid Mechanics 14 (2012), no. 2, 383-405.
	W. Rusin, Navier-Stokes equations, stability and minimal perturbations of global solutions. Journal of Mathematical Analysis and Applications 386 (2012), no. 1, 115-124.
	W. Rusin and V. Sverak, Minimal initial data for potential Navier-Stokes singularities. Journal of Functional Analysis, 260 (2011), no. 3, 879-891.
	P.B. Mucha and W. Rusin, Zygmund spaces, inviscid limit and uniqueness of Euler flows. Communications in Mathematical Physics 280 (2008), no. 3, 831-841.
	W. Rusin, On the inviscid limit for the solutions of two-dimensional incompressible Navier-Stokes equations with slip-type boundary conditions. Nonlinearity 19 (2006), no. 6, 1349-1363.