Skip to main content
Log in

Stationary Vortex Fluid Motions and the Maximum Principle

  • Research Articles
  • Published:
Russian Journal of Mathematical Physics Aims and scope Submit manuscript

Abstract

The goal of the present paper is to refine and supplement information about the solvability of the equation \(\Delta u=f(u)\) and the properties of its solutions by using the maximum principle.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  1. L. D. Landau and E. M. Lifshitz, Fluid Mechanics, Pergamon Press, London, England, 1987.

    Google Scholar 

  2. M. A. Lavrentiev and B. V. Shabat, Hydrodynamics Problems and Their Mathematical Models, Nauka, Moscow, Russia, 1977.

    Google Scholar 

  3. V. I. Arnol’d, “Conditions for Nonlinear Stability of Stationary Plane Curvilinear Flows of an Ideal Fluid”, Sov. Math. Doklady, 6 (1965), 773–777.

    MATH  Google Scholar 

  4. M. I. Vishik and S. B. Kuksin, “Perturbations of Quasilinear Elliptic Equations and Fredholm Manifolds”, Sbornik Mathematics, 58:1 (1987), 223–243.

    Article  ADS  MathSciNet  Google Scholar 

  5. V. A. Kondrat’ev and A. A. Kon’kov, “On Properties of Solutions of a Class of Nonlinear Second-Order Equations”, Sbornik Mathematics, 83:1 (1995), 67–77.

    Article  ADS  MathSciNet  Google Scholar 

  6. E. Mitidieri and S. I. Pokhozhaev, “A Priori Estimates and Blow-Up of Solutions to Nonlinear Partial Differential Equations and Inequalities”, Proc. of Steklov Inst. of Math., 234 (2001), 1–362.

    MATH  Google Scholar 

  7. S. I. Pokhozhaev, “Critical Nonlinearities in Partial Differential Equations”, Russian J. of Math. Phys., 20:4 (2013), 476–491.

    Article  ADS  MathSciNet  Google Scholar 

  8. R. Courant, Partial Differential Equations, Interscience Publishers, Geneva, Switzerland, 1962.

    MATH  Google Scholar 

  9. A.V. Bitsadze, Equations of Mathematical Physics, Nauka, Moscow, Russia, 1982.

    MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to S. A. Stepin.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Stepin, S.A. Stationary Vortex Fluid Motions and the Maximum Principle. Russ. J. Math. Phys. 28, 389–397 (2021). https://doi.org/10.1134/S1061920821030110

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1134/S1061920821030110

Navigation