On the two-dimensional initial boundary value problem for the Navier-Stokes equations with discontinuous boundary data

Journal Article · Sat Aug 05 00:00:00 EDT 1995 · Journal of Mathematical Sciences

DOI:https://doi.org/10.1007/BF02362947· OSTI ID:107573

Solonnikov, V A

We consider the initial boundary value problem for the Navier-Stokes equations with boundary conditions {rvec {nu}}{vert_bar}{partial_derivative}{omega} = {rvec a}. We assume that {rvec a} may have jump discontinuities at finitely many points {epsilon}1,{hor_ellipsis},{epsilon}m of the boundary {partial_derivative}{omega} of a boundary domain {omega} {contained_in} {Re}{sup 2}. We prove that this problem has a unique generalized solution in a finite time interval or for small initial and boundary data. The solution is found in a class of vector fields with infinite energy integral. The case of a moving boundary is also considered.

• Sponsoring Organization: USDOE
• OSTI ID: 107573
• Journal Information: Journal of Mathematical Sciences, Journal Name: Journal of Mathematical Sciences Journal Issue: 6 Vol. 75; ISSN 1072-1964; ISSN JMTSEW
• Country of Publication: United States
• Language: English

Related Subjects

42 ENGINEERING
66 PHYSICS
99 GENERAL AND MISCELLANEOUS
BOUNDARY-VALUE PROBLEMS
MOVING-BOUNDARY CONDITIONS
NAVIER-STOKES EQUATIONS
TWO-DIMENSIONAL CALCULATIONS